Practice Test

1) Pick out the only vector quantity in the following list :

2) A man can swim with a speed of 4 kmph in still water. He crosses a river 1 km wide that flows steadily at 3 kmph. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?

3) In a harbour, wind is blowing at the speed of 72 kmph and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km / h to the north, what is the direction of the flag on the mast of the boat?

4) A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

5) For any arbitrary motion, which of the following relations are true

6) A scalar quantity is one that

7) At what minimum altitude should the pilot fly the plane to avoid being hit.

8) The resultant of two forces 3 P and 2 P is R. If the first force is doubled, then the resultant is also doubled. The angle between the two forces is

9) The maximum height attained by an oblique projectile does not depend upon

10) Statement 1 : A person can swim in still water with a velocity less than river flow. If he starts swimming perpendicularly to the river velocity observed by stationary frame, the drift of the person is minimum.
Statement 2 : The time spent in river will be minimum, when swimmer swims in the direction perpendicular to the velocity of river.

11) The time of flight of a projectile on an upward inclined plane depends upon

12) Two bullets are fired horizontally, simultaneously and with different velocities from the same place. Which bullet will hit the ground earlier?

13) A projectile rises to a height of 10 m above and then falls at a distance 30 m away from the point of projection. Its vertical displacement is

14) In the case of an oblique projectile, the velocity is perpendicular to acceleration

15) A monkey can jump a maximum horizontal distance of 20 m. Then the velocity of the monkey is

16) A projectile is projected with kinetic energy of 800 J. If is has the maximum possible horizontal range, then its kinetic energy at the highest point will be

17) Statement 1 : A swimmer is swimming in the river for the shortest path. His average velocity is perpendicular to the water flow.
Statement 2 : The component of the resultant velocity of swimmer in the direction of flow should be least for shortest path.

18) The speed of projectile projected from the bottom is

19) The ratio of the speed of the projectile projected from the top and the speed of the projectile projected from the bottom of tower is

20) The time of flight of projectiles is

21) A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is

22) If a particle moves in a circle describing equal angles in equal times, its velocity vector

23) A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v. If the string is released, the stone flies

24) A body is moving in a circular path with a constant speed. It has

25) A motor cyclist going round in a circular track at constant speed has

26) A particle P is moving in a circle of radius 'a' with a uniform speed v. C is the center of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

27) A car moving on a horizontal road may be thrown out of the road in taking a turn

28) A particle moves with constant angular velocity in a circle. During the motion its

29) A stone tied to a string is rotated in a circle. If the string is cut, the stone flies away from the circle because

30) A body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then which of the following statement is true

31) When a body moves with a constant speed along a circle

32) A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant

33) On a railway curve, the outside rail is laid higher than the inside one so that resultant force exerted on the wheels of the rail car by the tops of the rails will

34) If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be

35) A cyclist taking turn bends inwards while a car passenger taking same turn is thrown outwards. The reason is

36) A car sometimes overturns while taking a turn. When it overturns, it is

37) A tachometer is a device to measure

38) Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

39) The ratio of angular speeds of minute hand and hour hand of a watch is

40) A car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud, as it leaves the ground are thrown

41) A particle is moving in a horizontal circle with constant speed. It has constant

42) A train is moving towards north. At one place it turns towards north-east, here we observe that

43) The angular speed of a fly wheel making 120 revolutions/minute is

44) A particle is moving on a circular path with constant speed, then its acceleration will be

45) A mass of 100 gm is tied to one end of a string 2 m long. The body is revolving in a horizontal circle making a maximum of 200 revolutions per min. The other end of the string is fixed at the centre of the circle of revolution. The maximum tension that the string can bear is (approximately)

46) A road is 10 m wide. Its radius of curvature is 50 m. The outer edge is above the lower edge by a distance of 1.5 m. This road is most suited for the velocity

47) Certain neutron stars are believed to be rotating at about 1 rev/sec. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be

48) A particle revolves round a circular path. The acceleration of the particle is

49) The length of second's hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is

50) An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m. The acceleration of a point on the tip of the blade is about

51) The force required to keep a body in uniform circular motion is

52) Cream gets separated out of milk when it is churned, it is due to

53) A particle of mass m is executing uniform circular motion on a path of radius r. If p is the magnitude of its linear momentum. The radial force acting on the particle is

54) A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance 'r'. The speed of the particle is

55) The average acceleration vector for a particle having a uniform circular motion is

56) When a particle moves in a uniform circular motion. It has

57) A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

58) A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

59) The magnitude of the centripetal force acting on a body of mass m executing uniform motion in a circle of radius r with speed v is

60) A string breaks if its tension exceeds 10 newtons. A stone of mass 250 gm tied to this string of length 10 cm is rotated in a horizontal circle. The maximum angular velocity of rotation can be

61) A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is

62) A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved

63) A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2 radian/sec. The centripetal force is

64) A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be

65) The second's hand of a watch has length 6 cm. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

66) A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done in full horizontal circle is

67) A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path

68) Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2

69) A car when passes through a convex bridge exerts a force on it which is equal to

70) The angular speed of seconds needle in a mechanical watch is

71) The angular velocity of a particle rotating in a circular orbit 100 times per minute is

72) A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

73) A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is

74) An unbanked curve has a radius of 60 m. The maximum speed at which a car can make a turn if the coefficient of static friction is 0.75, is

75) A wheel completes 2000 revolutions to cover the 9.5 km. distance. then the diameter of the wheel is

76) A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be

77) The centripetal acceleration is given by

78) A cylindrical vessel partially filled with water is rotated about its vertical central axis. It's surface will

79) If a particle covers half the circle of radius R with constant speed then

80) An aeroplane is flying with a uniform speed of 100 m/s along a circular path of radius 100 m. the angular speed of the aeroplane will be

81) A body moves with constant angular velocity on a circle. Magnitude of angular acceleration

82) A stone is tied to one end of a string 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone

83) A 100 kg car is moving with a maximum velocity of 9 m/s across a circular track of radius 30 m. The maximum force of friction between the road and the car is

84) The maximum speed of a car on a road-turn of radius 30 m, if the coefficient of friction between the tyres and the road is 0.4, will be

85) The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is

86) A particle of mass M is moving in a horizontal circle of radius R with uniform speed V. When it moves from one point to a diametrically opposite point, its

87) A ball of mass 0.1 Kg. is whirled in a horizontal circle of radius 1 m. by means of a string at an initial speed of 10 R.P.M. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is

88) If a cycle wheel of radius 4 m completes one revolution in two seconds. Then acceleration of a point on the cycle wheel will be

89) In uniform circular motion, the velocity vector and acceleration vector are

90) If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is

91) A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statement about the velocity of the car is true

92) A scooter is going round a circular road of radius 100 m at a speed of 10 m/s. The angular speed of the scooter will be

93) A particle of mass M moves with constant speed along a circular path of radius r under the action of a force F. Its speed is

94) In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

95) A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

96) A car is moving with high velocity when it has a turn. A force acts on it outwardly because of

97) A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

98) An athlete completes one round of a circular track of radius 10 m in 40 sec. The distance covered by him in 2 min 20 sec is

99) A particle is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point

100) In uniform circular motion

101) When a body moves in a circular path, no work is done by the force since,

102) A person with his hands in his pockets is skating on ice at the velocity of 10 m/s and describes a circle of radius 50 m. What is his inclination with vertical

103) If the radius of curvature of the path of two particles of same masses are in the ratio 1 : 2, then in order to have constant centripetal force, their velocity, should be in the ratio of

104) An object is moving in a circle of radius 100 m with a constant speed of 31.4 m/s. What is its average speed for one complete revolution

105) A body of mass 1 kg tied to one end of string is revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string will be

106) The acceleration of a train travelling with speed of 400 m/s as it goes round a curve of radius 160 m, is

107) A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then maximum velocity with which the car can move is

108) A 500 kg crane takes a turn of radius 50 m with velocity of 36 km/hr. The centripetal force is

109) In case of uniform circular motion which of the following physical quantity do not remain constant

110) A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be

111) A stone ties to the end of a string 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone

112) A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel?

113) What is the angular velocity of earth

114) If the length of the second's hand in a stop clock is 3 cm the angular velocity and linear velocity of the tip is

115) In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be

116) A block of mass m at the end of a string is whirled round in a vertical circle of radius R. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

117) A sphere is suspended by a thread of length l. What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension

118) A bottle of sodawater is grasped by the neck and swing briskly in a vertical circle. Near which portion of the bottle do the bubbles collect

119) A cane filled with water is revolved in a vertical circle of radius 4 meter and the water just does not fall down. The time period of revolution will be

120) A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed. The speed of the stone is 4 m/sec. The tension in the string will be 52 N, when the stone is

121) A body slides down a frictionless track which ends in a circular loop of diameter D, then the minimum height of the body in term D of so that it may just complete the loop, is

122) A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

123) The maximum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius l

124) The tension in the string revolving in a vertical circle with a mass m at the end which is at the lowest position

125) A hollow sphere has radius 6.4 m. Minimum velocity required by a motor cyclist at bottom to complete the circle will be

126) A fan is making 600 revolutions per minute. If after some time it makes 1200 revolutions per minute, then increase in its angular velocity is

127) A particle is tied to 20 cm long string. It performs circular motion in vertical plane. What is the angular velocity of string when the tension in the string at the top is zero

128) A stone tied with a string, is rotated in a vertical circle. The minimum speed with which the string has to be rotated

129) For a particle in a non-uniform accelerated circular motion

130) A fighter plane is moving in a vertical circle of radius 'r'. Its minimum velocity at the highest point of the circle will be

131) A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolutions per minute. The total tension in the string when the stone is at its lowest point is

132) A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is

133) When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)

134) A body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration, when the string is horizontal will be

135) A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical

136) A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height 'h' from the bottom, the particle will leave the sphere

137) A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle, is

138) A bucket full of water is revolved in vertical circle of radius 2 m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket

139) The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3 then its velocity is

140) For a particle in circular motion the centripetal acceleration is

141) A particle moves in a circular path with decreasing speed. Choose the correct statement.

142) A body of mass 1 kg is moving in a vertical circular path of radius 1 m. The difference between the kinetic energies at its highest and lowest position is

143) A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

144) A bullet is dropped from the same height when another bullet is fired horizontally. They will hit the ground

145) An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth's surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

146) A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

147) A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be

148) An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

149) A ball is rolled off the edge of a horizontal table at a speed of 4 m/second. It hits the ground after 0.4 second. Which statement given below is true

150) An aeroplane flying 490 m above ground level at 100 m/s, releases a block. How far on ground will it strike

151) A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is

152) A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread

153) If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

154) In the motion of a projectile freely under gravity, its

155) The angle of projection at which the horizontal range and maximum height of projectile are equal is

156) A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant

157) At the top of the trajectory of a projectile, the directions of its velocity and acceleration are

158) The velocity with which the projectile is projected is

159) The angle with the horizontal at which the projectile was projected is

160) The acceleration due to gravity is given by

161) The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it, will be

162) The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

163) At the top of the trajectory of a projectile, the acceleration is

164) A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

165) A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

166) If the range of a gun which fires a shell with muzzle speed V is R, then the angle of elevation of the gun is

167) If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be

168) A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

169) Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long–jump event

170) A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about

171) In a projectile motion, velocity at maximum height is

172) A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is

173) A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer)

174) Neglecting the air resistance, the time of flight of a projectile is determined by

175) The maximum horizontal range of a projectile is 400 m. The maximum value of height attained by it will be

176) A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

177) A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

178) A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

179) A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector is correctly shown in

180) A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

181) The driver of a car travelling at velocity v suddenly see a broad wall in front of him at a distance d. He should

182) Four persons K, L, M and N are initially at the corners of a square of side of length d. If every person starts moving, such that K is always headed towards L, L towards M, M is headed directly towards N and N towards K, then the four persons will meet after

183) A particle is moving eastwards with velocity of 5 m/s. In 10 sec the velocity changes to 5 m/s northwards. The average acceleration in this time is

184) Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower?

185) Assertion : Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.
Reason :The maximum height of projectile is independent of particle mass.

186) Assertion : The maximum horizontal range of projectile is proportional to square of velocity.
Reason :The maximum horizontal range of projectile is equal to maximum height attained by projectile.

187) Assertion : The trajectory of projectile is quadratic in y and linear in x.
Reason : y component of trajectory is independent of x-component.

188) Assertion : When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same time.
Reason :Horizontal velocity has no effect on the vertical direction.

189) Assertion : When the velocity of projection of a body is made n times, its time of flight becomes n times.
Reason : Range of projectile does not depend on the initial velocity of a body.

190) Assertion : The height attained by a projectile is twenty five percent of range, when projected for maximum range.
Reason : The height is independent of initial velocity of projectile.

191) Assertion : In order to hit a target, a man should point his rifle in the same direction as target.
Reason : The horizontal range of the bullet is dependent on the angle of projectile with horizontal direction.

192) Assertion : When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes.
Reason : The centripetal acceleration in circular motion is dependent on angular velocity of the body.

193) Assertion : During a turn, the value of centripetal force should be less than the limiting frictional force.
Reason : The centripetal force is provided by the frictional force between the tyres and the road.

194) Assertion : When a vehicle takes a turn on the road, it travels along a nearly circular path.
Reason : In circular motion, velocity of vehicle remains same.

195) Assertion : As the frictional force increases, the safe velocity limit for taking a turn on an unbanked road also increases.
Reason :Banking of roads will increase the value of limiting velocity.

196) Assertion : If the speed of a body is constant, the body cannot have a path other than a circular or straight line path.
Reason :It is not possible for a body to have a constant speed in an accelerated motion.

197) Assertion : In circular motion, work done by centripetal force is zero.
Reason : In circular motion centripetal force is perpendicular to the displacement.

198) Assertion : In circular motion, the centripetal and centrifugal force acting in opposite direction balance each other.
Reason : Centripetal and centrifugal forces don’t act at the same time.

199) Assertion : If both the speed of a body and radius of its circular path are doubled, then centripetal force also gets doubled.
Reason : Centripetal force is directly proportional to both speed of a body and radius of circular path.

200) Assertion : When an automobile while going too fast around a curve overturns, its inner wheels leave the ground first.
Reason : For a safe turn the velocity of automobile should be less than the value of safe limit velocity.

201) Assertion : A safe turn by a cyclist should neither be fast nor sharp.
Reason : The bending angle from the vertical would decrease with increase in velocity.

202) Assertion : Improper banking of roads causes wear and tear of tyres.
Reason : The necessary centripetal force is provided by the force of friction between the tyres and the road.

203) Assertion : Cream gets separated out of milk when it is churned, it is due to gravitational force.
Reason : In circular motion gravitational force is equal to centripetal force.

204) Assertion : Two similar trains are moving along the equatorial line with the same speed but in opposite direction. They will exert equal pressure on the rails.
Reason : In uniform circular motion the magnitude of acceleration remains constant but the direction continuously changes.

205) Assertion : A coin is placed on phonogram turn table. The motor is started, coin moves along the moving table.
Reason : The rotating table is providing necessary centripetal force to the coin.

206) Roads are banked on curves so that

207) In uniform circular motion

208) A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will

209) A body is revolving with a uniform speed v in a circle of radius r. The tangential acceleration is

210) A particle does uniform circular motion in a horizontal plane. The radius of the circle is 20 cm. The centripetal force acting on the particle is 10 N. It's kinetic energy is

211) A body of mass is suspended from a string of length . What is
minimum horizontal velocity that should be given to the body in its lowest position so that it may complete one full revolution in the vertical plane with the point of suspension as the centre of the circle

212) If the angular velocity is doubled, keeping radius the same, the new force will be

213) If the angular velocity is kept same but the radius of the path is halved, the new force will be

214) If the centripetal force F is kept constant but the angular velocity is doubled, the new radius of the path (original radius R) will be

215) A body of mass m kg is rotating in a vertical circle at the end of a string of length r metre. The difference in the kinetic energy at the top and the bottom of the circle is

216) A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth's surface will be

217) At the highest point of the path of a projectile, its

218) A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

219) When a body moves in a circular path, no work is done by the force since

220) If the sum of the two unit vectors is also a unit vector, then magnitude of their difference is

221) The magnitude of resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of the sides of an equilateral triangle taken in order is

222) When a body moves in a circular path, no work is done by the force since,

223) The angle of projection at which the horizontal range and maximum height of projectile are equal is

224) A particle is moving on a circular path with constant speed, then its acceleration will be

225) A particle is moving with a constant speed v in a circle. What is the magnitude of average after half rotation?

226) The radio of angular speeds of minute hand and hour hand of a watch is

227) A cane filled with water is revolved in a vertical circle of radius 4 m and the water just does not fall down. The time period of revolution will be

228) The angular speed of seconds needle in a mechanical watch is

229) If the length of the second’s hand in a stop clock is 3 cm the angular velocity and linear velocity of the tip is

230) A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change

231) Which of the following statements is false for a particle moving in a circle with a constant angular speed?

232) A particle moves in a circular path with decreasing speed. Choose the correct statement

233) A hollow sphere has radius 6.4 m. Minimum velocity required by a motor cyclist at bottom to complete the circle will be

234) A car sometimes overturns while taking a turn. When it overturns, it is

235) A car of mass 1000 kg moves on a circular track of radius 20 m. If the coefficient of friction is 0.64, then the maximum velocity with which the car can move is

236) A projectile is thrown with a speed u at an angle θ to the horizontal. The radius of curvature of its trajectory when the velocity vector of the projectile makes an angle α with the horizontal is

237) A projectile is thrown at angle β with vertical. It reaches a maximum height H. The time taken to reach the highest point of its path is

238) A stone is thrown at an angle θ to the horizontal reaches a maximum height H. Then the time of flight of stone will be

239) A body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration, when the string is horizontal will be

240) If a particle covers half the circle of radius R with constant speed then

241) A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved?

242) A bullet is fired with a velocity u making an angle of 60° with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is

243) The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5:3 the the velocity is

244) A body is projected from the earth at angle 30° with the horizontal with some initial velocity. If its range is 20 m, the maximum height reached by its is (in metre )

245) Neglecting the air resistance, the time of flight of a projectile is determined by

246) An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio

247) A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is tripled, it will just slip, if its distance from the centre is

248) A coin is placed on a gramophone record rotating at a speed of 45 rpm. It flies away when the rotational speed is 50 rpm. If two such coins are placed over the other on the same record, both of them will fly away when rotational speed is

249) A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path

250) A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following

251) Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

252) A projectile is fired with a velocity v at right angle to the slope which is inclined at an angle θ with the horizontal. What is the time of flight?

253) A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane it follows that

254) A boy whirl is a stone in a horizontal circle of radius 1.5 m and at height 2.0 m above level ground. The string breaks and the stone flies off tangentially and strikes the ground after traveling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion?

255) A particle is moving along a circular path with a uniform speed. How does its angular velocity change when it completes half of the circular path?

256) A particle does uniform circular motion in a horizontal plane. The radius of the circle is 20 cm. The centripetal force acting on the particle is 10 N. It’s kinetic energy is

257) In the case of an oblique projectile, the velocity is perpendicular to acceleration

258) If the angle of projection of a projectile is 30°, then how many times the horizontal range is larger than the maximum height?

259) Roads are banked on curves so that

260) A coin placed on a rotating turn table just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turn table is doubled, it will just slip at a distance of

261) A bomb is dropped from an aeroplane moving horizontally at constant speed. When air resistance is taken into consideration, the bomb

262) One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is

263) A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap respectively is

264) In a circus stuntman rides a motorbike in a circular track of radius R in the vertical plane. The minimum speed at highest point of track will be

265) A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25N. What is the maximum speed with which the ball can be moved?

266) In a projectile motion, velocity at maximum height is

267) A body is acted upon by a constant force directed towards a fixed point. The magnitude of the force varies inversely as the square of the distance from the fixed point. What is the nature of the path?

268) What is the angular velocity of earth?

269) A body of mass 2 kg attached to a string is whirled in a vertical circle of radius 5 m. The minimum speed of the body at lowest point so that the cord does not slacken even at the highest point is

270) A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular loop. The average velocity and average speed for each circular loop respectively is

271) The bob of a pendulum of mass m and length L is displaced, 90° from the vertical and gently released. In order that the string may not break upon passing through the lowest point, its minimum strength must be

272) When a body moves with a constant speed along a circle

273) A cyclist moves in such a way that he track 60° turn after 100 m. What is the displacement when to takes seventh turn?

274) A ball of mass 0.1 kg. Is whirled in a horizontal circle of radius 1 m. By means of a string at an initial speed of 10 R.P.M. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is

275) A fan is making 600 revolutions per minute. If after some time it makes 1200 revolutions per minute, then increase in its angular velocity is

276) A particle moves in a circular path with decreasing speed. Choose the correct statement.

277) A stone is tied to one end of a string and rotated in a horizontal circle with a uniform angular velocity. Let T be the tension in the string. If the length of the string is halved and its angular velocity is doubled, tension in the string will be

278) A sphere is suspended by a thread of length l. What minimum horizontal velocity has to be imparted the ball for it to reach the height of the suspension

279) If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height

280) A particle is projected from the ground with an initial speed of v at an angle θ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

281) The tension in the string revolving in a vertical circle with a mass m at the end which is the lowest position

282) The ratio of the angular speed of minutes hand and hour hand of a watch is

283) A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 s for every circular lap. The average velocity and average speed for each circular lap is

284) A cyclist turns around a curve at 15 miles/hour. If the turns at double the speed, the tendency to overturn is

285) On an unbanked road, a cyclist negotiating a bend of radius r at velocity v leans inwards by an angle

286) Two tall buildings are 40 m apart. With what speed must a ball be thrown horizontally from a window 145 m above the ground in one building, so that it will enter a window 22.5 m from the ground in the other?

287) A wheel rotates with a constant angular velocity of 300 rpm. The angle through which the wheel rotates in one second is

288) A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be

289) A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

290) A stone is thrown with a velocity v making an angle θ with the horizontal. At some instant, its velocity V is perpendicular to the initial velocity v. Then V is

291) The coordinates of a moving particle at any time 't' are given by x=αt^3 and y=βt^3. The speed of the particle at time 't' is given by

292) If the length of the second’s hand in a stop-clock is 3 cm, the angular velocity and linear velocity of the tip is

293) A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

294) A string of length l is fixed at one end and caries a mass m at the other end. The string makes 2/Ï€ rps around a vertical axis through the fixed end. What is the tension in string?

295) A particle of mass m moves with constant speed along a circular path of radius r under the action of a force F. Its speed is

296) The string of a pendulum of length l is displaced through 90° from the vertical and released. Then the minimum strength of the string in order to withstand the tension as the pendulum passes through the mean position is

297) Velocity vector and acceleration vector in a uniform circular motion are related as

298) Two projectiles thrown from the same point at angles 60° and 30° with the horizontal attain the same height. The ratio of their initial velocities is

299) A body is projected at such angle that the horizontal range is three times the greatest height. The angel of projection is

300) A stone is thrown at an angle θ to the horizontal reaches a maximum heights H . then the time of flight of stone will be

301) What should be the angular velocity of earth so that a body on its equator is weightless?

302) A particle is moving in a circle with uniform speed v. In moving from a point to another diametrically opposite point

303) If the range of a gun which fires a shell with muzzle speed V is R, then the angle of elevation of the gun is

304) On the centre of a frictionless table a small hole is made, through which a weightless string of length 2l is inserted. On the two ends of the string two balls of the same mass m are attached. Arrangement is made in such a way that half of the string is on the table top and half is hanging below. The ball on the table top is made to move in a circular path with a constant speed v. What is the centripetal acceleration of the moving ball

305) The maximum and minimum tension in the string whirling in a circle of radius 2.5 m with constant velocity are in the ratio 5 : 3 then its velocity is

306) A body of mass 1 kg is moving in a vertical circular path of radius 1 m. The difference between the kinetic energies at its highest and lowest point is

307) The angle of projection of a projectile for which the horizontal range and maximum height are equal is

308) A sphere of mass 0.2 kg is attached to an inextensible string of length 0.5 m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be

309) A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum with respect to the vertical

310) A particle is moving in a circle of radius R with constant speed v. If radius is doubled, then its centripetal force to keep the same speed gets

311) A ball is projected with kinetic energy E at an angle of 45° to the horizontal. At the highest point during its flight, its kinetic energy will be

312) The string of pendulum of length l is displaced through 90° from the vertical and released. Then the minimum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is

313) A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread

314) A string breaks if its tension exceeds 10 newtons. A stone of mass 250 gm tied to this string of length 10 cm is rotated in a horizontal circle. The maximum angular velocity of rotation can be

315) A stone is tied to one end of a string 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone

316) With what minimum speed a particle be projected from the origin so that it is able to pass through a given point (30 m, 40 m)?

317) The angular speed of a car increases from 600 rpm to 1200 rpm in 10 s. What is the angular acceleration of the car?

318) Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal acceleration is

319) A particle is projected with a speed v at 45° with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is

320) The simple sum of two co-initial vectors is 10 units. Their vector sum is 8 units. The resultant of the vectors is perpendicular to the smaller vector. The magnitudes of the two vectors are

321) A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

322) A mass of 2 kg is whirle‘d in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant, the tension in the string is double. The new speed is nearly

323) A particle performing uniform circular motion has

324) A stone tied to a string of length L is whirled in a vertical circle, with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of change in its velocity as it reaches a position, where the string is horizontal is

325) A cycle wheel of radius 0.4 m completes one revolution in one second then the acceleration of a point on the cycle wheel will be

326) Two projectiles A and B are thrown with velocities v and v/2 respectively. They have the same range. If B is thrown at an angle of 15° to the horizontal, a must have been thrown at an angle

327) The angular speed of a fly wheel making 120 revolutions/minute is

328) The sum of the magnitudes of two forces acting at a point is 16 N. the resultant of these forces is perpendicular to the smaller force has a magnitude of 8 N. If the smaller force is magnitude x, then the value of x is

329) A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

330) A projectile is projected with a speed u making an angle 2θ with the horizontal. What is the speed when its direction of motion makes an angle θ with the horizontal

331) A glass marble projected horizontally from the top of a table falls at a distance x from the edge of the table. If h is the height of the table, then the velocity of projection is

332) A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn’t fall of the bucket

333) If KE of the particle of mass m performing UCM in a circle of radius r is E. Find the acceleration of the particale

334) A particle of mass 100 g tied to a string is rotated along circle of radius 0.5 m. The breaking tension of string is 10 N. The maximum speed with which particle can rotated without breaking the string is

335) A boy is hanging from a horizontal branch of a tree. The tension in the arms will be maximum when the angle between the arms is

336) If the body is moving in a circle of radius r with a constant speed v, its angular velocity is

337) One end of a string of length l is connected to a particle of mass m and other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is

338) A body of mass m is projected at an angle of 45° with the horizontal. If air resistance is negligible, then total change in momentum when it strikes the ground is

339) At the point of a projectile motion, acceleration and velocity are perpendicular to each other?

340) A particle is moving in a circular path with a constant speed v. If θ is the angular displacement, then starting from θ=0°, the maximum and maximum changes in the momentum will occur, when value of θ is respectively

341) Two paper screens A and B are separated by a distance of 200 m. A bullet pierces A and then B. The hole in B is 40 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is

342) A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v. If the string is released, the stone flies

343) If a cycle wheel of radius 4 m completes one revolution in two seconds. Then acceleration of a point on the cycle wheel will be

344) Two particles are projected simultaneously in the same vertical plane, from the same point, both with different speeds and at different angles with horizontal. The path followed by one, as seed by the other, is

345) A projectile is thrown at angle β with vertical. It reaches a maximum height H. The time taken to reach the highest point of its path is

346) A body is tided with a string and is given a circular motion with velocity v in radius r. The magnitude of the acceleration

347) When a simple pendulum is rotated in a vertical plane with constant angular velocity, centripetal force is

348) Which of the following sets of factors will affect the horizontal distance covered by an athlete in a long-jump event

349) What is the angular velocity of earth

350) Ratio between maximum range and square of time of flight in projectile motion is

351) An airplane, diving at an angle of 53.0° with the vertical releases a projectile at an altitude of 730 m. The projectile hits the ground 5.00 s after being released. What is the speed of the aircraft?

352) A body of mass m hangs at one end of a string of length l, the other end of which is fixed. It is given a horizontal velocity so that the string would just reach where it makes an angle of 60° with the vertical. The tension in the string at mean position is

353) A stone tied to the end of a string 1m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone

354) A body of mass m is suspended from a string of length l. What is minimum horizontal velocity that should
be given to the body in its lowest position so that it may complete one full revolution in the vertical plane
with the point of suspension as the centre of the circle.

355) A man projects a coin upwards from the gate of a uniformly moving train. The path of coin for the man will be

356) An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m.
When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

357) A particle is thrown above, the correct v-t graph will be

358) An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth’s surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

359) A wheel completes 2000 revolutions to cover the 9.5 km. distance. Then the diameter of the wheel is

360) If the magnitude of the sum of the two vectors is equal to the difference of their magnitudes, then the angle between vectors is

361) A toy cyclist completes one round of a square track of side 2 m in 40 s. What will be the displacement at the end of 3 min?

362) Two bodies are projected with the same velocity. If one is projected at an angle of 30° and the other at an angle of 60° to the horizontal, the ratio of the maximum heights reached is

363) The kinetic energy of a projectile at the highest point is half of the initial kinetic energy. What is the angle of projection with the horizontal?

364) In uniform circular motion

365) A stone is tied at one end of a 5m long string and whirled in a vertical circle. The minimum speed required to just cross the topmost position is

366) A particle of mass m moves with constant speed along a circular path of radius r under the action of force F. Its speed is

367) A small cone filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down. What must be the maximum period of revolution?

368) In uniform circular motion, the velocity vector and acceleration vector are

369) An object of mass 10 kg is whirled round a horizontal circle of radius 4 m by a revolving string inclined 30° to the vertical. If the uniform speed of the object is 5 ms-¹ the tension in the string (approximately) is

370) A particle is projected up from a point at an angle with the horizontal. At any time t if p=linear momentum, y=vertical displacement, x=horizontal displacement, then the kinetic energy (K) of the particle plotted against these parameters can be

371) A stone of mass 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be

372) The speed of revolution of a particle going around a circle is doubled and its angular speed is halved. What happens to the centripetal acceleration?

373) A body moving along a circular path of radius R with velocity v, has centripetal accelerationa. If its velocity is made equal to 2v, then its centripetal acceleration is

374) The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

375) In above question, if the centripetal force F is kept constant but the angular velocity is doubled, the new radius of the path (original radius R) will be

376) A small block is shot into each of the four tracks as shown below. Each of the frictionless track rises to the same height. The speed, which the block enters the tracks, is same in all cases. At the highest point of the track, normal reaction is maximum in

377) A bullet is fired horizontally with a velocity of 80 ms-¹. During the first second,

378) A cricketer hits a ball with a velocity 25 m/s at 60° above the horizontal. How far above the ground it passes over a fielder 50 m from the bat (assume the ball is struck very close th the ground)

379) An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is

380) A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is

381) A particle is projected with speed v at an angle θ(0<θ<π/2) above the horizontal from a height H above the ground. If v= speed with which particle hits the ground and t=time taken by particle to reach ground, then

382) An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R. To hit a target which is R/2 from the gun and on the same level, the elevation angle of the gun should be

383) A car moving with the speed of 10 m/s takes a circular turn of radius 20 m. The magnitude of the acceleration of the car is

384) Centripetal acceleration is

385) A body crosses the topmost point of a vertical circle with critical speed. What will be its acceleration when the string is horizontal?

386) A particle is moving in a horizontal circle with constant speed. It has constant

387) A bend in a level road has a radius of 80 m. Find the maximum speed which a car turning the bend may have without skidding, if μ=0.25

388) A body of mass 100 g is rotating in a circular path of radius r with constant velocity. The work done in one complete revolution is

389) A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is

390) Neglecting the air resistance, the time of flight of a projectile is determined by

391) A car when passes through a convex bridge exerts a force on it which is equal to

392) The time period of the second’s hand of a watch is

393) A particle is tied to 20cm long string. It performs circular motion in vertical plane. What is the angular velocity of the string when the tension in the string at the top is zero

394) A body just being revolved in a vertical circle of radius R with a uniform speed. The string breaks when the body is at the highest point. The horizontal distance covered by the body after the string breaks is

395) An aeroplane is flying with a uniform speed of 100 m/s along a circular path of radius 100 m. the angular speed of the aeroplane will be

396) A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is

397) A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length l. The system is rotated about the other end of the spring with an angular velocity ω, in gravity free space. As shown in figure the increase in length of the spring will be

398) A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break

399) Three particles A, B and C are projected from the same point with the same initial speeds making angles30°, 45° and 60° respectively with the horizontally. Which of the following statements is correct?

400) A sphere is suspended by thread of length l.The minimum horizontal velocity which has to be imparted to the sphere for it reach the height of suspension is

401) A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with
speed of 5 m/sec from the same height. The correct statement is

402) Two stones thrown at different angles have same initial velocity and same range. If H is the maximum height attained by one stone thrown at an angle of 30°, then the maximum height attained by the other stone is

403) A ball of mass m is thrown vertically upwards. Another ball of mass 2m is thrown at an angle θ with the vertical. Both of them stay in air for same period of time. The heights attained by the two balls are in the ratio of

404) A projectile of mass m is thrown with a velocity v making an angle of 45° with the horizontal. The change in momentum from departure to arrival along vertical direction, is

405) A mass m is attached to the end of a rod of length l. The mass goes along a vertical circular path with the other end hinged at its centre. What should be the minimum velocity of the mass at the bottom of the circle so that the mass completes the circle?

406) what happens to the centripetal acceleration of a particle,when its speed is doubled and angular velocity is halved.

407) A cannon of a level plane is aimed at an angle θ above the horizontal and a shell is fired muzzle velocity v0 towards a cliff D distance away. The height at which the canon strikes the cliff is given by

408) A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is

409) At the top of the trajectory of a projectile, the direction of its velocity and acceleration are

410) An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960 m. When it is vertically above a point A on the ground a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

411) A body of mass 1 kg tied to one end of string is revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string will be

412) A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels

413) A particle moves in a circle of radius 30 cm. Its linear speed is given by v=2t where t in second and v in m/s. Find out its radial and tangential acceleration at t=3 sec respectively

414) A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

415) An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft position 10 s apart is 30°, then the speed of the aircraft is

416) A body moves with constant angular velocity on a circle. Magnitude of angular acceleration

417) A projectile is projected with kinetic energy K. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be

418) A scooter is going round a circular road of radius 100 m at a speed of 10 m/s. The angular speed of the scooter will be

419) A body of mass 5 kg is whirled in a vertical circle by a string 1 m long. Calculate velocity at the top of the circle for just looping the vertical loop

420) A cricketer can throw a ball to a maximum horizontal distance of 100 m. The speed with which he throws the ball is (to the nearest integer)

421) A body executing uniform circular motion has at any instant its velocity vector and acceleration vector

422) The average acceleration vector for a particle having a uniform circular motion is

423) A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

424) A body can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be

425) A curved road of 50 m radius is banked at correct angle for a given speed. If the speed is to be doubled keeping the same banking angle, the radius of curvature of the road should be changed to

426) In the above question, if the angular velocity is kept same but the radius of the path is halved, the new force will be

427) In resultant of which of the following sets of forces can not be zero

428) A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force F. If the angular velocity is doubled keeping radius the same, the new force will be

429) A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

430) A grass hopper finds that he can jump a maximum horizontal distance of 1 m. With what speed can be travel along the path if he speeds a negligible time on the ground

431) A car takes a turn around a circular curve. If it turns at double the speed, the tendency to overturn is

432) The horizontal range of an oblique projectile is equal to the distance through which a projectile has to fall freely from rest to acquire a velocity equal to the velocity of projection in magnitude. The angle of projection is

433) A body of mass m tied to a string is moved in a vertical circle of radius r. The difference in tensions at the lowest point and the highest point is

434) A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

435) A wheel of radius 1m rolls forward half a revolution on a horizontal ground. The magnitude to the displacement of the point of the wheel initially in contact with the ground is

436) A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height 'h' from the bottom, the particle will leave the sphere

437) In case of uniform circular motion which of the following physical quantity do not remain constant

438) what happens to centripetal
acceleration of particle when its speed is doubled and angular velocity is halved?

439) In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

440) A 100 kg car is moving with a maximum velocity of 9 m/s across a circular track of radius 30 m. The maximum force of friction between the road and the car is

441) If the radius of curvature of the path of two particles of same masses are in the ratio 1∶2, then in order to have constant centripetal force, their velocity, should be in the ratio of

442) A particle moves along a circle of radius [20/Ï€] m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

443) A wheel making 20 revolution per second is in a horizontal circle with a uniform angular velocity. Let T be the tension in the string. If the length of the string is halved and its angular velocity is doubled, tension in the string will be

444) A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is

445) The maximum speed of car on a road turn of radius 30m,if the coefficient of friction between tyres and the road is 0.4 ,will be

446) Toy cart tied to the end of an unstretched string of length a, when revolved moves in a horizontal circle of radius 2a with a time period T. Now the toy cart is speeded up until it moves in a horizontal circle of radius 3a with a period T'. If Hook’s law holds then

447) A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 m/s. At what angle from horizontal the ball must be fired so that it hits the pirate ship

448) A particle of mass m is projected with a velocity v making an angle of 45° with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height, is

449) A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has speed u. The magnitude of the
change in its velocity as it reaches a position where the string is horizontal is

450) A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω. The tension in the string if F. If the length of string and angular velocity are doubled, the tension is string is now

451) Two bodies are thrown up at angles of 45° and 60°, respectively with the horizontal. If both bodies attain same vertical height , then the ratio of velocities with which these are thrown is