Circular Motion ( Mcq ) 4r411v

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

MHT-CET QUESTIONS 1)

2)

A car is taking a turn on a level road. It may be thrown outwards because of the: a) weight b) lack of centripetal force c) reaction of the ground d) frictional force A body of mass m is moving with velocity v in uniform circular motion. The work done by the centripetal force in moving through half the circular path is : a)

m 2  r r

d)

m 2  2r r



In uniform circular motion : a) Both velocity and acceleration re constant b) Acceleration and speed are constant but velocity changes

7)

c) Both accleration and velocity

8)

d) Both decreases and speed is constant The uniform circular motion is accelerated motion, because a)

the motion accelerates due to the







a) r  FC b) FC  r c) zero d) None of these The angle between radius vector and centripetal acceleration is : a)

changes 4)

 force FC in circle of radius r is given by :

DNYANSAGAR A. Nagar

c) zero 3)

b)

m2  r 2 r

6)

curve, but the cyclist bends inwards while negotiating the same curv e. This happens because : a) the car is heavier than the cycle b) cyclist counteracts the centrifugal force, which throws the engers in the car outwards c) the cyucle has two wheels while the car has four wheels d) the cycle moves slower than the cars. Torque produced by the centripetal



2

rad

b)

3 rad 2

c) 2  rad d)  rad The angular displacement in circular motion is a) dimensional quantity b) dimensionless quantity c) unitless quantity and imensionless quantity d) unitless quantity

change in velocity b) the motion accelerates due to the change in angular velocity

Ans -

c) the motion accelerates due to the force 5)

d) all of these

(1 - b)

(2 - c)

(3 - c)

The engers in car are thrown outwards when the car negotiates a

(4 - a)

(5 - b)

(6 - c)

(7 - d)

(8 - b)

12

CIRCULAR MOTION


9)

10)

A particle moves along a circular path of constant radius. The magnitude of its acceleration is : a) uniform b) variable c) zero d) such as cannot be predicted from the given information A body of mass m is moving in a horizontal circle of radius ‘r’. If the centripetal force is F, the kinetic energy of the body is : a)

12)

13)

14)

b)

F.r

F.r 2 2

d)

F.r

16)

constant magnitude which is always perpendicular to the velocity of the particle. The motion takes place in a plane. It follows that : a) Its velocity is constant b) Its acceleration is constant c) Its motion is linear d) Its motion is circular The rate of change of angular velocity w.r. to t in uniform circular motion is a a) radial acceleration b) angular acceleration (  ) c) angular speed d) angular displacement What is the relation between tangential acceleration a T and the centripetal acceleration ac during non uniform circular motion? a) aT must be greater than ac b) aT must be less than ac c) aT must be equal to ac d) None of the above relations is true. A body of mass m is moving with uniform speed in a horizontal circle of

DNYANSAGAR A. Nagar

c) 11)

F.r 2

15)


A particle of mass m moving in a horizontal circle of radius r with a uniform speed v. When it moves from one point to diametrically oppsite point its: a) Kinetic energy changes by mv2/4 b) Momentum does not changes c) Momentum changes by 2mv d) Kinetic energy changes by mv2 The direction of angular displacement  in U.C.M. is given by a) left hand rule b) right hand thumb rule c) right handed screw rule d) either ‘a’ or ‘b’ A particle is moving on a ciruclar path with constant speed. Which of the following statements about the particle is true? a) It possesses radial acceleration b) It possesses radial velocity c) It possesses tangential acceleration d) It does not possess tangential velocity. A particle is acted upon by a force of

17)

radius r under a centripetal force

k , r2

where k is a constant. The K.E. of body is : a)

k2 r

b)

k 2r

c)

k r2

d)

k r

Ans -

13

(9 - d)

(10 - a)

(11 - c)

(12 - d)

(13 - a)

(14 - d)

(15 - b)

(16 - d)

(17 - b)

CIRCULAR MOTION


18)

A satellite of earth is revolving with

N. What can be the maximum angular

uniform speed v. If gravitational force

speed? a) 10 rad s-1 b) 100 rad s-1 c) 1000 rad s-1 d) 1 rad s-1 A particle revolves round the circular path with constant speed. The acceleration of particle is : a) Along the circumference of the circle b) Along the tangent c) Along the radius d) Zero If a particle goes round the circle once in a time period T, then the angular velocity  will be a) 2t b) T / 2 c) 2 / T d)  / T What determines the nature of the path followed by the particle? a) Speed b) Velocity c) Acceleration d) None of the above For a body moving in circular path of radius r with uniform speed the angle of banking is given by :

suddenly disapperas, the satellite will : a)

Continue tomove wit velocity v along

22)

the orginal orbit b) Moves with velocity v tangential to orbit c) Fall down with increasing velocity d) Ultimately come to rest somewhere n the orginal orbit 19)

23)

The infinitesimal angular displacement of a particle performing uniform

DNYANSAGAR A. Nagar

circular motion is a vector because a)

it obeys the cumulative and associative

24)

laws of vector addition

b) it do not obeys the laws of vector addition

c) it do not obeys the laws of multiplication of vectors

25)

d) all of these 20)

21)


Which of the following statements about the uniform rotatory motion along a circular path is true? a) Linear veolcity is uniform when angular velcoity is uniform b) Magnitude of acceleration is constant c) Acceleration is directed along the tangent to the ciruclar path d) None of the above statement is correct

a)

2 r.g

b)

tan -1

2 r.g

c)

2 r

d)

None of these

Ans (18 - b)

(19 - a)

(20 - b)

cm long is whirled in horizontal circle.

(21 - b)

(22 - c)

(23 - c)

If the string breaks under a force of 20

(24 - b)

(25 - b)

A body of mass 10 g tied to a string 20

14

CIRCULAR MOTION


26)

27)

28)

A wheel rotates about an axis ing through the centre and perpenducular to the plane with slowly incresing angular speed. it has : a) Radial velocity and radial acceleration b) Tangential velocity and radial acceleration c) Tangetial velocity and tangential acceleration d) Tangential velocity and acceleration having both tangential and radial components The relation between linear velocity and angular velocity of a body moving in circle in vector form is    a) v   b) v  r   r    c) v   d) r  v   /r Which of the following statements about the centripetal and centrifugal forces is correct? a) Centripetal force balances the

30)

31)

32)

c) half-way down the circle d) None of the above The work done by the centripetal force F when a body completes one revolution around a circle of radius R is : a) 2  RF b) 2 RF c) RF d) Zero What is the angular displacement of the minute hand in 20 minutes? a)  / 3 rad b) 2 / 3 rad c)  / 2 rad d) 3 / 2 rad A scooter is going around a circular road of radius 100m at a speed of 10 ms-1. What is the angular speed of the scooter? a) 10 rad s-1 b) 1 rad s-1 c) 0.1 rad s-1 d) 0.01 rad s-1 A body of mass m tied to a string of length r is at its lowest position. What should be the minimum speed given to it so as just to complete one revlolution?

DNYANSAGAR A. Nagar 33)

centrifugal force

b) Both centripetal force and centrifugal force act on the same body

34)

c) Centripetal; force is directed opposite to the centrifugal force d) Centripetal force is experienced by the observer at the centre of the ciruclar path described by the body. 29)


a)

gr

b)

3gr

c)

5 gr

d)

7 gr

Which of the following remains constant in UCM? a) Speed b) Kinetic energyKinetic energy c) Angular momentum d) All of these

A body of 1kg is tied to the end of a string 1 m long and whirled in a vertical circle

Ans -

with a constant speed of 4 m s-1. The tension in the string is 6.2 N. when the stone is : a) at the top of the circle b) at ther bottom of the circle 15

(26 - d)

(27 - a)

(28 - c)

(29 - a)

(30 - d)

(31 - b)

(32 - c)

(33 - c)

(34- d)

CIRCULAR MOTION


35)

36)

37)

A motor car is travelling 20 m/s on a circular road of radius 400 m. If it increases its speed at the rate of 1 m/s 2, then its acceleration will be a)

2 2 m/s2

b)

3 m/s 2

c)

2 m/s2

d)

3 3 m/s 2

39)

c) Instantaneous angular velocity 41)

To enable a particle describe a circular path, what should be the angle between its velocity and acceleration? a) 00 b) 450 c) 900 d) 1800 A body is to be slided without fricition along an inclined plane of height ‘h’ so that it loops the loop of radius ‘r’ at the bottom. The value of height is : a) h = 2r b) h = 4r

42)

d) None of the above A simple pendulum has a length l. What minimum velocity should be imparted to its bob at the mean position so that the bob reaches a height equal to above the point of suspension : a)

gl

b)

5 gl

c)

2 gl

d)

l g

Scalar product of radius vector and tangential velocity is : a) zero b) rv cos  c) rv sin  d) rv Centrifugal force is pseudo force because a) it is not provided by any real force but it arises due to accelerated frame of reference b) origin can not imaginary c) its direction is outwards along radius d) its magnitude is equal to centripetal force A flywheel rotates at a constant speed of 3000 rpm. The angle described by the shaft in radian in one second is : a) 2  b) 30  c) 100  d) 3000 

DNYANSAGAR A. Nagar

c) h = 5r 38)


d)

h=

43)

5 r 2

Earth is slightly bulge at equator so shape of earth is oblate spheroid. This is because at equator : a) Gravitational force is maximum b) Angular velocity is maximum c) Centrifugal force is maximum d) Above statement is worng If a stone is tied to a string and whirled in a circle, then the centripetal force would provides a) tension in the string b) mass of the string

44)

c) weight of string

Ans -

d) mass of stone 40)

All the magnitudes of which of the following can be treated as vectors? a)

Angular displacement

b) Average angular velocity

(35 - c)

(36 - c)

(37 - d)

(38 - c)

(39 - a)

(40 - c)

(41 - b)

(42 - a)

(43 - a)

(44 - c) 16

CIRCULAR MOTION


45)

46)

47)

48)

49)

50)

A stone tied to string is whirled then the string breaks at certain speed because: a) Gravitational force is maximum b) The required centripetal force is greater than tension sustainable by the string c) Required centripetal force is equal to tension in the string d) Centripetal force is equal to weight The driver of a car travelling at velocity v suddenly sees a broad wall in front of him at a distance ‘a’. He should a) brake sharply b) turn sharply c) both ‘a’ and ‘b’ d) none The angular speed of the hour hand of the clock is : a) 2  rad s-1 b) 2  rad minute-1 c) 2  rad day-1 d) None of the above In a circus a motor-cyclist rides along a circular track of radius r in a vertical circle, the minimum speed at the highest point in order to avoid a fall is:

51)

52)


d) None of the above A cyclist moves round a circular road of radius 50 metres. If the coefficient of friction between the tyres and road is 0.2, the maximum velocity with which he can go round without skidding is (g = 10m s-2) : a) 5 m s-1 b) 10 m s-l c) 20 m s-1 d) 7.5 m s-1 A stone of mass m is tied to a string of length L, and rotated in a circle with constant speed v, if the string is released the stone flies : a) Radially outward b) Radially inward c) Tangentially d) With an acceleration mv2/L A scooter is going around a circular track with a speed of 20 ms-1. The radius of the ciruclar track is 50m. The angular velocity of the scooter is : a) 0.4 rad s-1 b) 2.5 rad s-1 c) 8 rad s-1 d) 1000 rad s-1 A motor cyclist moves round a curve at a certain speed. He doubles his speed. The ratio of the tangents of the angles by which he leans with vertical in two cases is : a) 1:2 b) 4:1 c) 1: 4 d) 2:1.

DNYANSAGAR A. Nagar

a)

2 gr

b)

5 gr

c)

3 gr

d)

gr

53)

54)

The centripetal force is real force which provides with the real interacting force of a) mechanical b) electrical c) magnetic or gravitational d) All of these The angular speed of the munute hand of the clock in degrees per second is : a) 0.01 b) 0.1 c) 1.0

Ans (45 - b)

(46 - a)

(47 - d)

(48 - d)

(49 - d)

(50 - b)

(51 - b)

(52 - c)

(53 - a)

(54 - c) 17

CIRCULAR MOTION


55)

A spirit level is placed at the edge of a turn table along its radius. The bubble

61)

will be a)

at the centre of the container

b) at the outer edge of the container c) at the inner edge of the container 62)

d) will oscillate about the centre of the container 56)

57)

58)

59)

60)

One radian is approximately equal to : a) 1800 b) 570 c) 900 d) 3600 A particle covers equal distances around a circular path in equal intervals of time. It has uniform non zero rate of change of : a) linear displacement b) angular displacement c) linear velocity d) angular velocity When a cyclist takes a circular turn he leans: a) inward b) outward c) backward d) forward. A ball of mass 0.25kg 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? a) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s In a vertical circle of radius r, at what point in its path, particle has tension equal to zero? a) Highest point b) Lowest point


c) Any point d) Horizontal point A particle is moving around a circular path with uniform angular speed  . The radius of the circular path is r. The acceleration of the particle is : a)  2/r b)  2/r c) r  2 d) r2  A stone of mass m tied to a string is rotated in a circle of radius r with angular velocity  . The force of tension trying to break the string is : a)

mrw

b)

m2 r

c)

m r2

d)

None of these.

2


64)

The string of a conical pendulum will become horizontal when : a) Speed of revolution is zero b) Speed of revolution is almost infinite c) Speed of revolution is low d) Speed of revolution is very low A particle moves along a circular path of radius r with uniform speed  . The angle described by the particle in one second is given by : a)  r-1 b)  -1r c)  r-2 d)  2r

Ans (55 - c)

(56 - b)

(57 - b)

(58 - a)

(59 - a)

(60 - a)

(61 - c)

(62 - a)

(63 - b)

(64 - a) 18

CIRCULAR MOTION


65)

66)

67)

68)

69)

70)

Centrifugal machines make use of which of the following forces for their action: a) gravitational force b) frictional force c) centrifugal force d) viscous force A motor cycle is going on an over bridge of radius R. The driver maintains a constant speed. As motor cycle is ascending on the over bridge, the normal force on it : a) Increases b) Decreases c) Remains the same d) Fluctuates - erratically The angular acceleration of a particle moving along a circular path with uniform speed is : a) uniform but non zero b) zero c) variable d) such as cannot be predicted from the given information Cream is separated from the milk because: a) cream is heavier than skimmed milk b) cream is 1ighter than skimmed milk c) cream is more viscous d) None of the above. What determines the nature of path followed by the particle? a) Speed b) Velocity c) Acceleration d) None of these A body of mass 10 kg is moving in a circle of radius 1 m with an angular velocity of 2 rad/s. The centripetal force is a) 10 N b) 40 N

71)

72)


c) 30 N d) 20 N A particle is describing the circular path of radius 10m every 2s. The average angular speed of the particle, during 4s is : a) 2  rad s-1 b) 4  rad s-1 c) 20  rad s-1 d) None of the above A man going on a cycle round a circular track of length 34.3 metres completes one round in 22 sec. The angle through which he leans inward is : a) 30° b) 60° c) 45° d) 20° If a particle moves in a circle describing equal angles in equal times in aplane about a fixed point, its velocity vector : a) Remains constant b) Changes in magnitude c) Changes in direction d) Changes both in magnitude and direction A particle is moving along a circular path with uniform speed. What is the angle between its instantaneous velocity and acceleration? a) 00 b) 450 c) 900 d) 1800


74)

Ans (65 - c)

(66 - b)

(67 - b)

(68 - b)

(69 - b)

(70 - d)

(71 - d)

(72 - c)

(73 - c)

(74 - c) 19

CIRCULAR MOTION


75)

76)

77)

78)

The string of a conical pendulum will become horizontal when: a) speed of revolution is zero . b) speed of revolution is almost infinite c) speed of revolution is low d) speed of revolution is very high An aeroplane is taking a turn in a horizontal plane. While doing so, it a) remains horizontal b) inclines inwards c) inclines outwards d) makes wings vertical In half period of revolution displacement and the distance covered is : a) 2r,  r b) 2  r, 2r c)  r, 2r d) zero, 2  r A car is going around a circle of radius R1 with constant speed. Another car is going around a circle of radius R2 with constant speed. If both a them take same time to complete the circles, the ratio of their angular speeds will be :

80)

82)

balances his weight c) He loses weight some how d) The force exerted by the surrounding A car moves on a circular road. It describes equal angles about the centre in equal intervals of time. Which of the following statements about the velocity of the car is true? a) Velocity is constant b) Magnitude of velocity is constant but direction changes c) Both magnitude and direction of velocity change d) Velocity is directed towards the centre of the circle. A car is moving on a curved bridge of radius r with velocity v. The maximum velocity with which it can move round it without leaving the bridge at the highest point is :

DNYANSAGAR A. Nagar

a) 79)

81)


R1 / R2

b)

83)

a)

v  gr

b)

v  5 gr

c)

v  2 gr

d)

v = gr

A car is moving along the horizontal banked curved road. At banked curve road, the normal reaction is

R 1 / R2

a)

c) R12 / R22 d) 1 An iron ball is moving from rim to rim via lowest point at the bottom of a small hemispherical bowl of radius 10cm. The velocity with which the ball es from the lowest position is : (g = 9.8 m s-2) a) 14 m s-1 b) 140m s-1 c) 1.4 m s-1 d) 0.7 m s-l A motor cyclist rides around the well with a round vertical wall and does not fall down while riding becuase : a) The force of gravity disappears b) The frictional force of the wall

equal to weight

b) greater than weight c) less than weight d) less than or equal to weight

Ans -

20

(75 - b)

(76 - b)

(77 - c)

(78 - d)

(79 - c)

(80 - b)

(81 - b)

(82 - a)

(83 - b)

CIRCULAR MOTION


84)

85)

86)

87)

88)

89)

A particle is revolving in a circle, clockwise in the plane of the paper. The angular acceleration is directed : a) Towards the centre in the plane of the paper b) Radially outwards in the plane of the paper c) Perpendicular to the plane of the paper d) Vertically in the plane of the paper A particle is moving along a circular path with uniform speed. Throgh what angle does its angular velocity change when it completes half of the circular path? a) 00 b) 450 c) 1800 d) 360 One kg stone tied to a metre long string is whirled in a vertical circle with 4 m s-1. The tension is 6 N at (g = 10m s-2): a) top of circle b) bottom of circle c) half way down d) None of these. A body moving in a circular path with constnt speed has : a) constant retardation b) variable acceleration c) radially outward acceleration d) constant acceleration A bucket full of water is rotated in a vertical circle. The water does not spill because the weight of water: a) provides the necessary centripetal force b) provides the centrifugal force c) provides the viscous force d) cancels the force of surface tension If a body of mass 1000 gm is tied to free end of string of length 100 cm and whirled in a horizontal circle in a


second, then the tensionin the string will be a)

4 2 N

b)

2 2 N

c) 3 2 N d) 2 N If the fingers of the right hand are curled in the sense of motion of the particle performing circular motion then the outstretched thumb gives the direction of : a) Angular velocity, Angular acceleration b) Tangential velocity c) Tangential acceleration d) Linear velocity The length of the second hand of a watch is 10mm. What is the change in the angular speed of the watch after 15 seconds? a) Zero b) (10  /2) mm s-1 c) (20/  ) mm s-1 d) 10 2 mm s-1 For a car moving along circular road of radius r and with coefficient of friction  between the tyres and the road, the maximum velocity without skidding is:

90)


92)

a)

v  rg

b)

v  rg

c)

v  2rg

d)

None of these.

Ans -

21

(84 - c)

(85 - a)

(86 - a)

(87 - b)

(88 - a)

(89 - a)

(90 - a)

(91 - a)

(92 - b)

CIRCULAR MOTION


93)

94)

95)

96)

97)

98)


as it es through the lowest point in its path? a) b) 9.8 m/s 2 m/s c) 4.43 m/s d) 1 / 2 m/s 99) A particle covers equal distances around a circular path in equal intervals of time. Which of the following quantities connected with the motion of the particle remains constant with time? a) Displacement b) Velocity c) Speed d) Acceleration 100) A body is tied to a string and is whirled in the vertical circle of radius r. The velocity of the body is maximum : a) at the highest point b) at the lowest point c) at a point in level with the centre horizontally d) None of the above. 101) A particle moves in a circular path 0.4m in radius with constant speed. If particle makes 5 revolutions in each second of its motion the speed of the particle is : a) 10.6 m/s b) 12.56 m/s c) 11.2 m/s d) 13.6 m/s 102) If a cyclist doubles his speed while negotiating a curve, how does the tendency to overturn vary? a) Remains unchanged b) Doubled c) Halved d) Ouadrupled

An important consequence of centrifugal force is that the earth is : a) Spheroid b) Sphere c) Oblate spheroid d) Circular A coin kept on a horizontal rotating disc has its centre at a distance of 0.25 m from the aixs of rotationof the disc. If  is 0.2, then the angular velocity of the disc at which the coin will slip off, ( g= 9.8 m/ s2 ) a) 3.8 rad/s b) 2.8 rad/s c) 4.8 rad/s d) 5.8 rad/s Two satellites are going around the earth at a height of 200 km and 300 km respectively. If angular speed of both is same, the centripetal acceleration will be : a) same for both b) more for the first c) more for the second d) dependent on the mass of the satellite A scooterist is moving round a circular track of radius 480 m. The track is 1 m wide. If his speed is 72 km/hour, how much the outer edge of track is lifted to bank the track for him? (g = 10 m s-2) a) 10cm b) 50cm c) 8.3cm d) 4.1cm The angular velocity of a wheel is 70 rad/ s/ If the radius of the wheel is 0.5m, then its linear velocity will be : a) 10 m/s b ) 35 m/s c) 20 m/s d) 70 m/s A pendulum bob on a 2 m string is displaced 600 from the vertical and then released. What is the speed of the bob

DNYANSAGAR A. Nagar

Ans (93 - c)

(94 - b)

(95 - c)

(96 - c)

(97 - b)

(98 - c)

(99 - c)

(100 - b)

(101 - b)

(102 - d) 22

CIRCULAR MOTION


103) 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 a) 2.5 m/s b) 8.57 m/s c) 6.5 m/s d) 3.5 m/s 104) A small body of mass m slides down a hemispherical smooth bowl from the rim to the bottom. The velocity of the body at the bottom is : a)

2 gr

b)

c)

 gr

d)

109)

110)

5 gr

None of these.


a) 6 mg b) 4 mg c) 2 mg d) 3 mg. A car is moving in a circular horizontal track of radius 10 m, with constant speed 10 m/s. A bob is suspended from roof of car with rod. Angle made by rod with vertical : (g = 9.8 m/s2) a) Zero b) 450 c) 300 d) 600 A can filled with water is revolved in vertical circle of radius 4 m and water just does not fall down at the highest point. The time period of revolution is(g= 9.87 m s-2) : a) 1 sec b) 2sec c) 4 sec d) 8 sec A simple pendulum of length 1 m, the bob performs circular motion in horizontal plane if its string making an angle 600 with the vertical, then the period of rotation of the bob will be ( g = 10 m/s2) a) 2 s b) 1.4 s c) 1.98 s d) 4 s A cyclist turns around a curve at 40 km/ hr. If he rounds the curve at double speed, his tendency to overturn is : a) Doubled b) Halved c) Tripled d) Quadrupled

DNYANSAGAR A. Nagar

105) A particle moves in a circle of radius 25 cm at two revolutions per second, the aceleration of particle in m/s2 is: a)  2 b) 4  2 c) 8  2 d) 2  2 106) The radius of the circular path of particle is doubled but its frequency of rotation remains unchanged. If the initial centripetal force be F, then the final value of the centripetal force will be : a) F b) 2F c) 4F d) F/2 107) A particle P is moving in a circle of radius ‘a’ with uniform velocity v.C. is centre of the circle and AB is adiameter. The angular velocity of P about A and C are in the ratio : a) 1 : 1 b) 2 : 1 c) 1 : 2 d) 4 : 1 108) A particle of mass m is rotating by means of a string in a vertical circle. The difference in the tensions at the bottom and the top would be:

111)

112)

Ans (103 - b)

(104 - a)

(105 - b)

(106 - b)

(107 - c)

(108 - a)

(109 - b)

(110 - c)

(111 - b)

(112 - d) 23

CIRCULAR MOTION


length 1 m, then the angle made by the rod with thetrack will be (g = 10 m/s2) a) zero b) 300 c) 450 d) 600 118) The string of a simple pendulum is horizontal at a given height and is released. The tension in the string at the lowest point is : a) T = mg b) T = 2 mg c) T = 3 mg d) T = 4 mg 119) In an atom two electrons move round the nucleus in circular orbits of radii R and 4R respectively, the ratio of time taken by them to complete one revolution is :

113) A disc revolves in a horizontal plane at the rate of 210 r.p.m. A coin placed at a distance of 2cm from the axis of rotation just remains at rest on the disc. The coefficient of friction between the disc and coin is (g = 10 m s-2) a) 0.97 b) 0.5 c) 0.35 d) 1 114) A person with his hands in his pocket is skating on ice at the rate of 10 m/s and describes a circle of radius 50 m. What is his inclination to the vertical? (g = 10 m/s2) 1I F G H2 JK 1I F G H5JK


3I F G H5JK 1I F G H10JK

DNYANSAGAR A. Nagar

a)

tan 1

c)

tan 1

b)

tan 1

d)

tan 1

115) A proton revolves round a circular path of radius 0.1 m. If it is acted upon by a force 4 x 10-13 N to keep it moving, the angular velocity of proton is (mp = 1.6 x 10-27kg): a) 5 x 107 rad s-1 b) 5 x 107 rad s-1 c) 5 rad s-1 d) 0.5 rad s-1 116) Amotor cyclist moving with velocity of 72 km/hr on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 m. In order to avoid skidding, he must bend w.r.t. the vertical plane by a n angle  greater than : (g = 10 m/s2) a)  = tan-1 (6) b)  = tan-1 (25.92) c)  = tan-1 (2) d)  = tan-1 (4) 117) A car is moving in a horizontal circular track of radius 10 m with a constant speed 10m/s. If a bob is suspended form the roof of the car by light rigid rod of

a)

1 4

b)

8 1

c)

4 1

d)

1 8

120) A motor car is travelling at 30 m s-1 on a circular curve of radius 500 m. It is increasing its speed at the rate of 2 m s-2, what is its acceleration? a) 2 m s-2 b) 1.8 m s-2 c) 2.7 m s-2 d) none of these 121) In a circus a rider rides in a circular track of radius R in vertical plane. The minimum velocity at the highest point of the track is : a) c)

2gR 2gR

b)

3gR

d)

gR

Ans -

24

(113 - a)

(114 - c)

(115 - a)

(116 - c)

(117 - c)

(118 - c)

(119 - d)

(120 - c)

(121 - d)

CIRCULAR MOTION



an angle of 600 with the vertical, its 122) A train is safely negotiating a curve of velocity is 2 m/s. The tension in the radius 500 m at a speed of 54 m hr-1. By how much should the outer rail be string in this position : (g = 9.8 m/s2) raised, if the distance between the two a) 0.4 N b) 0.89 N -2 rails is 1.5 m? (g = 10 m s ) c) 0.09 N d) 0.98 N a) 6.75 cm b) 15 cm 128) A weightless thread can tension c) 4.5 cm d) 2.5 cm upto 30 N.A. stone of mass 0.5 kg is tied 123) Kinetic energy of a body moving in to it and is revolved in a circular path vertical circle is of radius 2m in a vertical plane. If g = a) constant at all points on a circle 10 m/s 2, then the maximum angular b) different at different points on a velocity of the stone will be : circle a) 5 rad/s b) 30 rad/s c) zero at all the point on a circle d) negative at all the points c) d) 10 rad/s 60 rad/s 124) A motor car is travelling at 20 m/s on a 129) A pilot of mass 81 kg loops the loop with circular curve of radius 100 m. It is steady speed of 300 km/h. If the radius increasing its speed at the rate of 5 m/s2 is 0.5 km then the force with which the what is its acceleration? pilot is pressed into the seat at the a) 2 m/s2 b) 6.4 m/s2 highest point of the loop, is c) 4 m/s2 d) 9 m/s2 a) 3.15 x 102 N b) zero 125) When a particle is moved in a vertical c) 8.10 x 102 N d) 19.35 x 102 N circle a) it has constant radial and tangential 130) A mass of 100 g is tied to one end of a string 2 m long. Thebody is revolving acceleration in a horizontal circle making a b) it has variable tangential and radial maximum of 200 rpm. The outer end of acceleration c) it has only constant radiual acceleration string is fixed at the centre of d) it has only constant tangential revolution. The maximum tension the acceleration string can bear is approximately : 126) A ball of mass 0.25 kg attached to the end a) 8.76 N b) 8.94 N of a string of length 1.96 m is moving in c) 89.42 N d) 87.64 N 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? Ans a) 14 m/s b) 4 m/s (122 - a) (123 - b) (124 - b) c) 3.92 m/s d) 5 m/s 127) A particle of mass 100 g is tied to one (125 - b) (126 - a) (127 - b) end of string of length 1 m. It rotates in (128 - a) (129 - a) (130 - d) a vertical circle. When the string makes

DNYANSAGAR A. Nagar

25

CIRCULAR MOTION



circle, then the energy of the body at the highest position will be (g = 9.8 m/s2) a) 2.45 J b) 1.25 J c) 3.45 J d) 4.45 J 137) The maximum velocity at the lowest point, so that the string just slacks at highest point in a vertical circle of radius l, is :

131) A stone of mass 16 kg is attached to a string 144 m long and is whirled in a horizonal circle. The maxmium tension the string can stand is 16 newton. The maximum velocity of revolution that can be given to the stone without breaking it, will be : a) 20 ms-1 b) 16 ms-1 c) 14 ms-1 d) 12 ms-1 132) 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 the curve of 40 m radius without slipping if the road is unbanked should be : (g = 9.8 m/s2) a) 25 m/s b) 19 m/s c) 14 m/s d) 11 m/s 133) A weightless thread can bear tension upto 3.7 kg wt. A stone of mass 500g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 ms -2, then the maximum angular velocity of the stone will be : a) 4 rad/s b) 16 rad/s c) d) 2 rad/s 21 134) A boy on a cycle pedals around a circle of radius 20 m at a speed of 20 m/s. The combined mass of boy and the cycle is 90 kg. The angle that the cycle makes with vertical so that he may not fall : (g = 9.8 m/s2) a) 60.500 c) 63.900 b) 26.120 d) 30.000 135) A fighter plane is moving in a vertical circle of radius r. Its minimum velocity at the highest point of the circle will be:

a)

gl

b)

3 gl

c)

5 gl

d)

7 gl

138) The second hand of a watch has length 6cm. Speed of end point and magnitude of difference of velocities at two perpendicular position will be : a) 6.28 and 0 mm/s b) 8.88 and 4.44 mm/s c) 8.88 and 6.28 mm/s d) 6.28 and 8.88 mm/s 139) A 500 kg car takes round turn of radius 50m with a velocity of 36 km/h. The centripetal force is : a) 250 N b) 750 N c) 1000 N d) 1200 N 140) A hollow sphere has radius 6.4 m. Minimum velocity required by motor cyclist at bottom to complete the circle will be : a) 17.7 m/s b) 12.4 m/s c) 10.2 m/s d) 16.0 m/s

DNYANSAGAR A. Nagar

a)

3gr

b)

Ans -

2 gr

c) d) gr gr / 2 136) If a body of mass 0.1 kg tied with a string of length 1 m, is rotated in vertical

(131 - d)

(132 - c)

(133 - a)

(134 - c)

(135 - c)

(136 - a)

(137 - c)

(138 - d)

(139 - c)

(140 - a) 26

CIRCULAR MOTION


141) A stone of mass 1 kg tied to one end of a string of length 1m, is whirled in a horizontal circle with a uniform angular velocity of 2 rad/s. The tension (in N) in the string is : 2

b)

1 2

c) 4

d)

1 4

a)


c) 36 x 1021 N d) 3.6 x 109 N 146) Two racing cars of masses m1 and m2 are moving in circles of a radii r1 and r2 respectively. Their speeds are such that they each make a complete circle in the same length of time t. The ratio of the angular speed of the first to the second car is : a) m1 : m2 b) 1 : 1 c) r1 : r2 d) m1r1 : m2r2 147) Breaking tension in the string is 80 N. A body of mass 0.1 kg is attached to it and whirled in circle of radius 0.5m. What will be maximum period of revolution before string breaks?

142) A body of mass 2 kg attached to a cord and whirled in a vertical circle of radius 2 m. The minimum speed at the bottom of the circle so that the cord will not slacken when the body rounds the top of the circle will be ( g = 10 m/s2) a) 10 m/s b) 6.3 m/s c) 7 m/s d) 5 m/s 143) When angular velocity of a uniform 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 : a) 2.5 m/s2, 7.5 m/s2 b) 7.5 m/s2, 22.5 m/s2 c) 5 m/s2, 45 m/s2 d) 2.5 m/s2, 22.5 m/s2 144) 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 : a) its velociyt is constant b) in moves in a straight line c) its kinetic energy is constant d) its acceleration is constant 145) The earth (mass = 6 x 1024 kg) revolves round the sun with angular velocity 2 x 10-7 rad/s in circular orbit of radius 1.5 x 108 km. The force exerted by sun is: a) 3.6 x 1021 N b) 3.6 x 10-21 N

DNYANSAGAR A. Nagar a)

s

b)

 s 20

c)

 s 5

d)

 s 10

148) A tube of length L is completely filled with an incompressible liquid of mass m and closed at both ends. The tube is then rotated in horizontal plane about one of its end with uniform angular speed  . What is force exerted by liquid at the other end?

v

a)

mL2 2

c)

2

mL

b)

mL2 4

d)

mL2 8

Ans -

27

(141 - c)

(142 - a)

(143 - d)

(144 - c)

(145 - c)

(146 - a)

(147 - b)

(148 - a) CIRCULAR MOTION


149) The maximum speed with which a car can be safely driven along a curved road of radius 30 m and banked at 300 with horizontal : a) 130 m/s b) 14.00 m/s c) 1.303 m/s d) 13.03 m/s 150) Find the maximum velocity for overturning a car moved on a circular track of radius 100m. The coefficient of friction between the road and tyre is 0.2. a) 0.14 m/s b) 140 m/s c) 1.4 km/s d) 14 m/s 151) A coin placed on a rotating table just slips when placed at a distance 4r from the centre. On doubling he angular velocity of the table. The coin will just slip when distance from centre is equal to : a) 4r b) r c) 2r d) r/4 152) A particle of mass m describes a circle of radius r. The centripetal acceleration of the particle is 4/r2. What will be the momentum of the particle? a) 4 m/r b) 2 m/r c) 4 m / r d) 2 m/ r

154)

Std. - 12th (Science) 4

A

r

o

c

k

e

c

t

w

i

t

h

a

l

i

f

t

o

f

f

m

a

s

s

3

.

5

x

1

0

kg is blasted upwards with an initial accleration of 10 m/s2. Then the initial thrust of the blast is : a) 3.5 x 105 N b) 7.0 x 105 c) 14.0 x 105 N d) 1.75 x 105 N 155) In an atom two electrons moves round the nucleus in circular orbitsof radii R & 4R respectively the ratio of the time takan by them to complete one revolution is: a) 1/4 b) 4/1 c) 8/1 d) 1/8

*****

DNYANSAGAR A. Nagar

153) A bucket tied at the end of a 1.6 long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position? (Take g = 10 m/s2) a) 4 m/s b) 6.25 m/s c) 16 m/s d) None of the above

Ans (149 - d)

(150 - d)

(151 - b)

(152 - d)

(153 - a)

(154 - b)

(155 - d) 28

CIRCULAR MOTION

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