Practice Test

1) What are the angular speed and linear speed of the motion?

2) Is the acceleration vector a constant vector and what is its magnitude?

3) A cyclist speeding at v km / h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the tyres and the road is 0.1. The maximum speed of the cyclist for him not to slip is about

4) What is the maximum permissible speed to avoid slipping?

5) The tension in the string is

6) The speed of the stone is increased beyond the maximum permissible value and the string breaks suddenly. Which of the following correctly describes the trajectory of the stone after the string breaks :

7) You may have seen in a circus a motorcyclist driving in vertical loops inside a 'death well' (a hollow spherical chamber with holes, so the spectators can watch from outside). What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

8) A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis. The coefficient of frictions between the wall and his clothing is 0.15. The minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling), when the floor is suddenly removed, is

9) The centre of mass of a triangular lamina is at its

10) The centre of mass of one of the following shapes does not lie at its centre.

11) A flywheel gains a speed of 540 rpm in 6 seconds. Its angular acceleration is

12) The radius of the path of a body in uniform circular motion is doubled. The centripetal force needed, if its speed remains the same is

13) A fighter aircraft is looping in a vertical plane. The minimum velocity at the highest point is (Given : r = radius of circle)

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

15) The maximum possible projection for A is

16) The maximum possible projection for B is

17) The maximum possible projection for C is

18) Two boys of masses 40 kg and 60 kg are standing at the opposite ends of a boat of length 8 m and mass 120 kg in a river. What would be the displacement of the boat relative to water if the boys interchange their positions?

19) The maximum velocity at which a truck can safely travel without toppling over, on a curve of radius 250 m (the height of the centre of gravity of the truck above the ground is 1.5 m and the distance between the wheels is 1.5 m, the track being horizontal) is

20) Two skaters on frictionless ice hold opposite ends of a pole of negligible mass and length l. An axis runs along the pole, and the origin of the axis is at the centre of mass of the two-skater system. One skater, Fred, weighs twice as much as the other skater, Ethel. Where do the skaters meet if, Fred pulls hands over hand along the pole so as to draw himself to Ethel?

21) Statement 1 : On a circular turn without banking centripetal force is provided by friction force.
Statement 2 : Friction force acting on a vehicle on circular turn without banking is a balanced by other forces.

22) Statement 1 : Due to circular motion of a particle, a force arises which acts towards the centre. This is called centripetal force.
Statement 2 : Centripetal force is perpendicular to the velocity of particle performing circular motion.

23) Its maximum speed for which the contact with the road is not broken at the highest point is

24) The maximum uniform speed, it can maintain on the bridge if it does not lose contact anywhere on the bridge is

25) A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the centre. If the angular velocity of the turnable is doubled, it will just slip at t distance of

26) A mass of one kg is connected to a fixed point by a string 1 m in length and whirled in a horizontal circle in 1 second. The tension in the string is

27) When the bob of a simple pendulum passes through the position of equilibrium, the string is subjected to a tension equal to twice the weight of the bob. Through what maximum angle from the vertical can the pendulum be deflected?

28) A tube one metre long is filled with liquid of mass 1 kg. The tube is closed at both the ends and is revolved about one end in a horizontal plane at 2 rev/s. The force experienced by the lid at the other end is

29) When a bucket containing water is rotated fast in a vertical circle of radius R, the water in the bucket doesn't spill provided

30) A coin placed on a gramophone record rotating at 33 rpm flies off the record, it it is placed at a distance of more than 16 cm from the axis of rotation. If the record is revolving at 66 rpm, the coin will fly off if it is placed at a distance not less than

31) Where will be the centre of mass after removal of square 1?

32) Where will be the centre of mass after the removal of squares 1 and 2?

33) Where will be the centre of mass after the removal of squares 1 , 2 and 3?

34) Where will be the centre of mass after the removal of squares 1 and 3?

35) Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls while in air

36) Statement 1 : A particle is moving in such a way that normal acceleration is constant and its moduli is equal to the tangential acceleration. The path of the particle is spiral.
Statement 2 : When velocity increases radius of curvature increases for constant normal acceleration.

37) Two identical trains A and B are running from west to east and east to west at equator. They move with the same speed.
Statement 1 : Pressure exerted by B on the ground will be larger than pressure exerted by A.
Statement 2 : Both A and B move on circular tracks of radius equal to earth's radius.

38) The normal force by the wall on the block is

39) The frictional force by the wall is

40) The tangential acceleration of the block is

41) A particle moving in a plane is acted upon by a force of constant magnitude which is always perpendicular to the velocity the particle, then:

42) Assuming the coefficient of friction between the road and tyres of a car to be 0.5 the maximum speed with which the car can move round a curve of 40 m radius without slipping if the road is unbanked is:

43) 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:

44) A coin placed on a rotating table just slips when placed at a distance 4 r from the centre. On doubling the angular velocity of the table, the coin will just slip when the distance from the centre is equal to:

45) In the above question the magnitude of the instantaneous acceleration is:

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

47) A small block is placed at the top of a smooth sphere. What will be the angle made by the radius vector of the block with the horizontal when it just breaks off from the surface?

48) A disc revolves in a horizontal plane with a steady speed of 3 r.p.s. A coin just keeps on rotating with the disc when placed 2 cm from the axis of rotation. The coefficient of friction between the coin and disc is:

49) A mass of 2 kg is whirled in a horizontal circle at a speed of 5 revolutions/min. keeping the radius constant, the tension in the string is doubled. The new speed nearly is:

50) A swing is at 1 m height above the ground level in its lowermost position and 3 m in highest position. Its speed at lowest position is:

51) A can filled with water is revolved in a vertical circle of radius 4 m and the water does not fall down, the time period of revolution is about:

52) A motorcyclist double his velocity when he is having a turn. The force exerted outwardly will be:

53) The centre of a wheel rolling on a plane surface moves with a speed 'V'. A particle on the rim of the wheel at the same level as the centre will be moving at speed of:

54) A train moving with constant speed is taking a sharp circular turn on a horizontal track. A man throws a ball vertically up in the train. Then the ball will:

55) A particle describes horizontal circle on the smooth surface of an inverted cone at a height 9.8 cm above the vertex of the cone. The speed of the particle is:

56) The length of second hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is:

57) When the angular velocity of a uniformly rotating body has increased thrice the resultant of forces applied to it increases by 60 N. Find the acceleration of the body in two cases if the mass of the body is 3 kg.

58) A sphere of mass 100 g is attached to a string of length 1.3 m whose upper end is fixed to ceilings. The sphere is made to describe a horizontal circle of radius 50 cm. The time period of the revolution is:

59) A small disc is placed at the top of a hemisphere of radius R. What is the smallest horizontal velocity that should be given to the disc for it to leave the hemisphere without sliding down the sphere?

60) A boy is sitting on a joy wheel at a distance of 5 m from the centre. When the joy wheel is rotated, the boy just slips. If the coefficient of friction is 0.56 between the boy and the platform of the wheel, what is the speed of rotation?

61) A planet takes three earth years to complete the orbit round the sun. The orbit of the planet is coplanar with the earth. What will be the time taken by the planet to complete the orbit round the sun with respect to an observer on earth?

62) A body is allowed to slide down a frictionless track freely under gravity. The track ends in a semicircular shaped part of diameter D. What should be the height (minimum) from which the body must fall so that it completes the circle?

63) The coefficient of friction between tyres and road is 0.4, then maximum speed of the car on road turn of radius 30 m, will be:

64) A stone tied to a string of 80 cm is whirled in a horizontal circle with constant speed. If it makes 25 revolutions in 44.5 seconds, what is the acceleration of the stone?

65) Consider a point P at contact point of a wheel on ground which rolls on ground without slipping, then value of displacement of point P when wheel completes half of rotation. (if radius of wheel is 1 m):

66) Find the velocity of the particle moving in a circular path having a centripetal force of 10 N whose mass is 100 g and radius of circular path is 50 cm.

67) A 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?

68) A body is suspended from a smooth horizontal nail by a string of length 0.25 metre. What minimum horizontal velocity should be given to it in the lowest position so that it may move in a complete vertical circle with the nail at the centre?

69) A one kg stone attached to the end of a 60 cm chain is revolving at the rate of 3 revolutions/second. If after 30 seconds, it is making only one revolution per second, find the mean torque:

70) A small object placed on a rotating horizontal turn table just slips when it is placed at a distance of 4cm from the axis of rotation. If the angular velocity of the turn-table is doubled the object slips when its distance from the axis of rotation is:

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

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

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

74) An athlete completes one round of a circular track of radius R in 40 sec. His displacement at the end of 2 min. 20 sec will be:

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

76) A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between:

77) When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming the acceleration to be uniform, how many rotations it will make in next three seconds?

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