Circular Motion ( MCQ )

DNYANSAGARA. Nagar

1) A car is taking a turn on a level road. Itmay be thrown outwards because of the:a) weightb) lack of centripetal forcec) reaction of the groundd) frictional force

2) A body of mass m is moving withvelocity v in uniform circular motion.The work done by the centripetal forcein moving through half the circularpath is :

a) rr

m

2

b) 22

rr

m

c) zero d) rr

m

22

3) In uniform circular motion :a) Both velocity and acceleration re

constantb) Acceleration and speed are constant

but velocity changesc) Both accleration and velocity

changesd) Both decreases and speed is constant

4) The uniform circular motion isaccelerated motion, becausea) the motion accelerates due to the

change in velocityb) the motion accelerates due to the

change in angular velocityc) the motion accelerates due to the forced) all of these

5) The passengers in car are thrownoutwards when the car negotiates a

curve, but the cyclist bends inwardswhile negotiating the same curv e. Thishappens because :a) the car is heavier than the cycleb) cyclist counteracts the centrifugal

force, which throws the passengers inthe car outwards

c) the cyucle has two wheels while the carhas four wheels

d) the cycle moves slower than the cars.6) Torque produced by the centripetal

force CF

in circle of radius r is givenby :a) CFr

b) rFC

c) zero d) None of these7) The angle between radius vector and

centripetal acceleration is :

a)2 rad b)

32

rad

c) 2 rad d) rad8) The angular displacement in circular

motion is -a) dimensional quantityb) dimensionless quantityc) unitless quantity and imensionless

quantityd) unitless quantity

Ans -(1 - b) (2 - c) (3 - c)

(4 - a) (5 - b) (6 - c)

(7 - d) (8 - b)

MHT-CET QUESTIONS

12

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I Std. - 12th (Science)

CIRCULAR MOTION

Ans -(9 - d) (10 - a) (11 - c)

(12 - d) (13 - a) (14 - d)

(15 - b) (16 - d) (17 - b)

13

DNYANSAGARA. Nagar

9) A particle moves along a circular pathof constant radius. The magnitude of itsacceleration is :a) uniformb) variablec) zerod) such as cannot be predicted from the

given information10) A body of mass m is moving in a

horizontal circle of radius ‘r’. If thecentripetal force is F, the kinetic energyof the body is :

a) 2.F r

b) F . r

c)2.F 2r

d) r.F

11) A particle of mass m moving in ahorizontal circle of radius r with auniform speed v. When it moves fromone point to diametrically oppsite pointits:a) Kinetic energy changes by mv2/4b) Momentum does not changesc) Momentum changes by 2mvd) Kinetic energy changes by mv2

12) The direction of angular displacement in U.C.M. is given bya) left hand ruleb) right hand thumb rulec) right handed screw ruled) either ‘a’ or ‘b’

13) A particle is moving on a ciruclar pathwith constant speed. Which of thefollowing statements about the particleis true?a) It possesses radial accelerationb) It possesses radial velocityc) It possesses tangential accelerationd) It does not possess tangential velocity.

14) A particle is acted upon by a force of

constant magnitude which is alwaysperpendicular to the velocity of theparticle. The motion takes place in aplane. It follows that :a) Its velocity is constantb) Its acceleration is constantc) Its motion is lineard) Its motion is circular

15) The rate of change of angular velocityw.r. to t in uniform circular motion is aa) radial accelerationb) angular acceleration ( )c) angular speedd) angular displacement

16) What is the relation between tangentialacceleration aT and the centripetalacceleration ac during non uniformcircular motion?a) aT must be greater than acb) aT must be less than ac

c) aT must be equal to ac

d) None of the above relations is true.17) A body of mass m is moving with

uniform speed in a horizontal circle of

radius r under a centripetal force 2rk

,

where k is a constant. The K.E. of bodyis :

a)r

k 2

b) rk2

c) 2rk

d) rk


CIRCULAR MOTION

14


DNYANSAGARA. Nagar

CIRCULAR MOTION

18) A satellite of earth is revolving withuniform speed v. If gravitational forcesuddenly disapperas, the satellite will :a) Continue tomove wit velocity v along

the orginal orbit

b) Moves with velocity v tangential toorbit

c) Fall down with increasing velocityd) Ultimately come to rest somewhere n

the orginal orbit19) The infinitesimal angular displacement

of a particle performing uniformcircular motion is a vector becausea) it obeys the cumulative and associative

laws of vector additionb) it do not obeys the laws of vector

additionc) it do not obeys the laws of

multiplication of vectorsd) all of these

20) Which of the following statements aboutthe uniform rotatory motion along acircular path is true?a) Linear veolcity is uniform when

angular velcoity is uniformb) Magnitude of acceleration is

constantc) Acceleration is directed along the

tangent to the ciruclar pathd) None of the above statement is correct

21) A body of mass 10 g tied to a string 20cm long is whirled in horizontal circle.If the string breaks under a force of 20

N. What can be the maximum angularspeed?a) 10 rad s-1 b) 100 rad s-1

c) 1000 rad s-1 d) 1 rad s-1

22) A particle revolves round the circularpath with constant speed. Theacceleration of particle is :a) Along the circumference of the circleb) Along the tangentc) Along the radiusd) Zero

23) If a particle goes round the circle oncein a time period T, then the angularvelocity will bea) t2 b) 2/Tc) T/2 d) T/

24) What determines the nature of the pathfollowed by the particle?a) Speedb) Velocityc) Accelerationd) None of the above

25) For a body moving in circular path ofradius r with uniform speed the angleof banking is given by :

a) gr.

2b) tan -1

gr.

2

c)r

2d) None of these

Ans -(18 - b) (19 - a) (20 - b)

(21 - b) (22 - c) (23 - c)

(24 - b) (25 - b)

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DNYANSAGARA. Nagar

CIRCULAR MOTION

26) A wheel rotates about an axis passingthrough the centre and perpenducularto the plane with slowly incresingangular speed. it has :a) Radial velocity and radial accelerationb) Tangential velocity and radial

accelerationc) Tangetial velocity and tangential

accelerationd) Tangential velocity and acceleration

having both tangential and radialcomponents

27) The relation between linear velocityand angular velocity of a body movingin circle in vector form isa) rv

b) rv

c) rv / d) vr

28) Which of the following statements aboutthe centripetal and centrifugal forces iscorrect?a) Centripetal force balances the

centrifugal forceb) Both centripetal force and centrifugal

force act on the same bodyc) Centripetal; force is directed opposite

to the centrifugal forced) Centripetal force is experienced by the

observer at the centre of the ciruclarpath described by the body.

29) A body of 1kg is tied to the end of a string1 m long and whirled in a vertical circlewith a constant speed of 4 m s-1. Thetension in the string is 6.2 N. when thestone is :a) at the top of the circleb) at ther bottom of the circle

c) half-way down the circled) None of the above

30) The work done by the centripetal forceF when a body completes one revolutionaround a circle of radius R is :a) 2 RF b) 2 RFc) RF d) Zero

31) What is the angular displacement of theminute hand in 20 minutes?a) rad3/ b) rad3/2c) rad2/ d) rad2/3

32) A scooter is going around a circularroad of radius 100m at a speed of10 ms-1. What is the angular speed of thescooter?a) 10 rad s-1 b) 1 rad s-1

c) 0.1 rad s-1 d) 0.01 rad s-1

33) A body of mass m tied to a string oflength r is at its lowest position. Whatshould be the minimum speed given toit so as just to complete one revlolution?

a) gr b) gr3

c) gr5 d) gr7

34) Which of the following remainsconstant in UCM?a) Speedb) Kinetic energyKinetic energyc) Angular momentumd) All of these

Ans -(26 - d) (27 - a) (28 - c)

(29 - a) (30 - d) (31 - b)

(32 - c) (33 - c) (34- d)

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DNYANSAGARA. Nagar

CIRCULAR MOTION

35) A motor car is travelling 20 m/s on acircular road of radius 400 m. If itincreases its speed at the rate of 1 m/s2,then its acceleration will bea) 2m/s22 b) 2m/s3c) 2m/s2 d) 2m/s33

36) To enable a particle describe a circularpath, what should be the angle betweenits velocity and acceleration?a) 00 b) 450

c) 900 d) 1800

37) A body is to be slided without fricitionalong an inclined plane of height ‘h’ sothat it loops the loop of radius ‘r’ at thebottom. The value of height is :a) h = 2r b) h = 4r

c) h = 5r d) h = 25

r

38) Earth is slightly bulge at equator soshape of earth is oblate spheroid. Thisis because at equator :a) Gravitational force is maximumb) Angular velocity is maximumc) Centrifugal force is maximumd) Above statement is worng

39) If a stone is tied to a string and whirledin a circle, then the centripetal forcewould providesa) tension in the stringb) mass of the stringc) weight of stringd) mass of stone

40) All the magnitudes of which of thefollowing can be treated as vectors?a) Angular displacementb) Average angular velocity

c) Instantaneous angular velocityd) None of the above

41) A simple pendulum has a length l. Whatminimum velocity should be impartedto its bob at the mean position so thatthe bob reaches a height equal to abovethe point of suspension :

a) gl b) gl5

c) gl2 d) gl

42) Scalar product of radius vector andtangential velocity is :a) zero b) rv cos c) rv sin d) rv

43) Centrifugal force is pseudo forcebecausea) it is not provided by any real force but

it arises due to accelerated frame ofreference

b) origin can not imaginaryc) its direction is outwards along radiusd) its magnitude is equal to centripetal

force44) A flywheel rotates at a constant speed of

3000 rpm. The angle described by theshaft in radian in one second is :a) 2 b) 30c) 100 d) 3000

Ans -(35 - c) (36 - c) (37 - d)

(38 - c) (39 - a) (40 - c)

(41 - b) (42 - a) (43 - a)

(44 - c)

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DNYANSAGARA. Nagar

CIRCULAR MOTION

45) A stone tied to string is whirled then thestring breaks at certain speed because:a) Gravitational force is maximumb) The required centripetal force is

greater than tension sustainable by thestring

c) Required centripetal force is equal totension in the string

d) Centripetal force is equal to weight46) The driver of a car travelling at velocity

v suddenly sees a broad wall in front ofhim at a distance ‘a’. He shoulda) brake sharply b) turn sharplyc) both ‘a’ and ‘b’ d) none

47) The angular speed of the hour hand ofthe clock is :a) 2 rad s-1

b) 2 rad minute-1

c) 2 rad day-1

d) None of the above48) In a circus a motor-cyclist rides along a

circular track of radius r in a verticalcircle, the minimum speed at the highestpoint in order to avoid a fall is:

a) gr2 b) gr5

c) gr3 d) gr49) The centripetal force is real force which

provides with the real interacting forceofa) mechanicalb) electricalc) magnetic or gravitationald) All of these

50) The angular speed of the munute handof the clock in degrees per second is :a) 0.01b) 0.1c) 1.0

d) None of the above51) A cyclist moves round a circular road

of radius 50 metres. If the coefficient offriction between the tyres and road is0.2, the maximum velocity with whichhe 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

52) A stone of mass m is tied to a string oflength L, and rotated in a circle withconstant speed v, if the string is releasedthe stone flies :a) Radially outwardb) Radially inwardc) Tangentiallyd) With an acceleration mv2/L

53) A scooter is going around a circulartrack with a speed of 20 ms-1. The radiusof the ciruclar track is 50m. The angularvelocity 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

54) A motor cyclist moves round a curve ata certain speed. He doubles his speed.The ratio of the tangents of the anglesby which he leans with vertical in twocases is :a) 1:2 b) 4:1c) 1: 4 d) 2:1.

Ans -(45 - b) (46 - a) (47 - d)

(48 - d) (49 - d) (50 - b)

(51 - b) (52 - c) (53 - a)

(54 - c)

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DNYANSAGARA. Nagar

CIRCULAR MOTION

55) A spirit level is placed at the edge of a

turn table along its radius. The bubble

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

d) will oscillate about the centre of the

container56) One radian is approximately equal to :

a) 1800 b) 570

c) 900 d) 3600

57) A particle covers equal distances arounda circular path in equal intervals oftime. It has uniform non zero rate ofchange of :a) linear displacementb) angular displacementc) linear velocityd) angular velocity

58) When a cyclist takes a circular turn heleans:a) inward b) outwardc) backward d) forward.

59) A ball of mass 0.25kg attached to the endof a string of length 1.96 m is moving ina horizontal circle. The string willbreak, if the tension is more than 25 N.What is the maximum speed with whichthe ball can be moved?a) 14 m/s b) 3 m/sc) 3.92 m/s d) 5 m/s

60) In a vertical circle of radius r, at whatpoint in its path, particle has tensionequal to zero?a) Highest pointb) Lowest point

c) Any pointd) Horizontal point

61) A particle is moving around a circularpath with uniform angular speed . Theradius of the circular path is r. Theacceleration of the particle is :a) 2/r b) 2/rc) r 2 d) r2

62) A stone of mass m tied to a string isrotated in a circle of radius r withangular velocity . The force of tensiontrying to break the string is :

a) mrw2 b)r

m 2

c) 2rm

d) None of these.

63) The string of a conical pendulum willbecome horizontal when :a) Speed of revolution is zerob) Speed of revolution is almost

infinitec) Speed of revolution is lowd) Speed of revolution is very low

64) A particle moves along a circular pathof radius r with uniform speed . Theangle described by the particle in onesecond is given by :a) r-1 b) -1rc) 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)

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DNYANSAGARA. Nagar

CIRCULAR MOTION

65) Centrifugal machines make use of whichof the following forces for their action:a) gravitational forceb) frictional forcec) centrifugal forced) viscous force

66) A motor cycle is going on an over bridgeof radius R. The driver maintains aconstant speed. As motor cycle isascending on the over bridge, thenormal force on it :a) Increasesb) Decreasesc) Remains the samed) Fluctuates - erratically

67) The angular acceleration of a particlemoving along a circular path withuniform speed is :a) uniform but non zerob) zeroc) variabled) such as cannot be predicted from the

given information68) Cream is separated from the milk

because:a) cream is heavier than skimmed milkb) cream is 1ighter than skimmed milkc) cream is more viscousd) None of the above.

69) What determines the nature of pathfollowed by the particle?a) Speedb) Velocityc) Accelerationd) None of these

70) A body of mass 10 kg is moving in acircle of radius 1 m with an angularvelocity of 2 rad/s. The centripetal forceisa) 10 N b) 40 N

c) 30 N d) 20 N71) A particle is describing the circular

path of radius 10m every 2s. The averageangular speed of the particle, during 4sis :a) 2 rad s-1

b) 4 rad s-1

c) 20 rad s-1

d) None of the above72) A man going on a cycle round a circular

track of length 34.3 metres completesone round in 22 sec. The angle throughwhich he leans inward is :a) 30° b) 60°c) 45° d) 20°

73) If a particle moves in a circle describingequal angles in equal times in aplaneabout a fixed point, its velocity vector :a) Remains constantb) Changes in magnitudec) Changes in directiond) Changes both in magnitude and

direction74) A particle is moving along a circular

path with uniform speed. What is theangle between its instantaneous velocityand acceleration?a) 00 b) 450

c) 900 d) 1800

Ans -(65 - c) (66 - b) (67 - b)

(68 - b) (69 - b) (70 - d)

(71 - d) (72 - c) (73 - c)

(74 - c)

20


DNYANSAGARA. Nagar

CIRCULAR MOTION

75) The string of a conical pendulum willbecome horizontal when:a) speed of revolution is zero .b) speed of revolution is almost

infinitec) speed of revolution is lowd) speed of revolution is very high

76) An aeroplane is taking a turn in ahorizontal plane. While doing so, ita) remains horizontalb) inclines inwardsc) inclines outwardsd) makes wings vertical

77) In half period of revolutiondisplacement and the distance coveredis :a) 2r, r b) 2r, 2rc) r, 2r d) zero, 2r

78) A car is going around a circle of radiusR1 with constant speed. Another car isgoing around a circle of radius R2 withconstant speed. If both a them take sametime to complete the circles, the ratioof their angular speeds will be :

a) R R1 2/ b) R1 / R2

c) R12 / R2

2 d) 179) An iron ball is moving from rim to rim

via lowest point at the bottom of a smallhemispherical bowl of radius 10cm. Thevelocity with which the ball passes fromthe 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

80) A motor cyclist rides around the wellwith a round vertical wall and does notfall down while riding becuase :a) The force of gravity disappearsb) The frictional force of the wall

balances his weightc) He loses weight some howd) The force exerted by the surrounding

81) A car moves on a circular road. Itdescribes equal angles about the centrein equal intervals of time. Which of thefollowing statements about the velocityof the car is true?a) Velocity is constantb) Magnitude of velocity is constant but

direction changesc) Both magnitude and direction of

velocity changed) Velocity is directed towards the centre

of the circle.82) A car is moving on a curved bridge of

radius r with velocity v. The maximumvelocity with which it can move roundit without leaving the bridge at thehighest point is :

a) grv b) grv 5

c) grv 2 d) v = gr

83) A car is moving along the horizontal

banked curved road. At banked curve

road, the normal reaction is

a) equal to weight

b) greater than weight

c) less than weight

d) less than or equal to weight

Ans -(75 - b) (76 - b) (77 - c)

(78 - d) (79 - c) (80 - b)

(81 - b) (82 - a) (83 - b)

21


DNYANSAGARA. Nagar

CIRCULAR MOTION

84) A particle is revolving in a circle,clockwise in the plane of the paper. Theangular acceleration is directed :a) Towards the centre in the plane of the

paperb) Radially outwards in the plane of the

paperc) Perpendicular to the plane of the

paperd) Vertically in the plane of the paper

85) A particle is moving along a circularpath with uniform speed. Throgh whatangle does its angular velocity changewhen it completes half of the circularpath?a) 00 b) 450

c) 1800 d) 360

86) One kg stone tied to a metre long stringis whirled in a vertical circle with 4 ms-1. The tension is 6 N at (g = 10m s-2):a) top of circleb) bottom of circlec) half way downd) None of these.

87) A body moving in a circular path withconstnt speed has :a) constant retardationb) variable accelerationc) radially outward accelerationd) constant acceleration

88) A bucket full of water is rotated in avertical circle. The water does not spillbecause the weight of water:a) provides the necessary centripetal

forceb) provides the centrifugal forcec) provides the viscous forced) cancels the force of surface tension

89) If a body of mass 1000 gm is tied to freeend of string of length 100 cm andwhirled in a horizontal circle in a

second, then the tensionin the stringwill be

a) 4 2 N b) 2 2 N

c) 3 2 N d) 2 N90) If the fingers of the right hand are

curled in the sense of motion of theparticle performing circular motionthen the outstretched thumb gives thedirection of :a) Angular velocity, Angular

accelerationb) Tangential velocityc) Tangential accelerationd) Linear velocity

91) The length of the second hand of a watchis 10mm. What is the change in theangular speed of the watch after 15seconds?a) Zerob) (10/2) mm s-1

c) (20/) mm s-1

d) 10 2 mm s-1

92) For a car moving along circular road ofradius r and with coefficient of friction between the tyres and the road, themaximum velocity without skidding is:

a) rgv b) rgv

c) rgv 2 d) None of these.

Ans -(84 - c) (85 - a) (86 - a)

(87 - b) (88 - a) (89 - a)

(90 - a) (91 - a) (92 - b)

22


DNYANSAGARA. Nagar

CIRCULAR MOTION

93) An important consequence ofcentrifugal force is that the earth is :a) Spheroidb) Spherec) Oblate spheroidd) Circular

94) A coin kept on a horizontal rotating dischas its centre at a distance of 0.25 m fromthe aixs of rotationof the disc. If is 0.2,then the angular velocity of the disc atwhich the coin will slip off, ( g= 9.8 m/s2)a) 3.8 rad/s b) 2.8 rad/sc) 4.8 rad/s d) 5.8 rad/s

95) Two satellites are going around theearth at a height of 200 km and 300 kmrespectively. If angular speed of both issame, the centripetal acceleration willbe :a) same for bothb) more for the firstc) more for the secondd) dependent on the mass of the satellite

96) A scooterist is moving round a circulartrack of radius 480 m. The track is 1 mwide. If his speed is 72 km/hour, howmuch the outer edge of track is lifted tobank the track for him? (g = 10 m s-2)a) 10cm b) 50cmc) 8.3cm d) 4.1cm

97) The angular velocity of a wheel is 70 rad/s/ If the radius of the wheel is 0.5m, thenits linear velocity will be :a) 10 m/s b ) 35 m/sc) 20 m/s d) 70 m/s

98) A pendulum bob on a 2 m string isdisplaced 600 from the vertical and thenreleased. What is the speed of the bob

as it passes through the lowest point inits path?a) 2 m/s b) 8.9 m/sc) 4.43 m/s d) 2/1 m/s

99) A particle covers equal distances arounda circular path in equal intervals oftime. Which of the following quantitiesconnected with the motion of theparticle remains constant with time?a) Displacement b) Velocityc) Speed d) Acceleration

100) A body is tied to a string and is whirledin the vertical circle of radius r. Thevelocity of the body is maximum :a) at the highest pointb) at the lowest pointc) at a point in level with the centre

horizontallyd) None of the above.

101) A particle moves in a circular path 0.4min radius with constant speed. If particlemakes 5 revolutions in each second ofits motion the speed of the particle is :a) 10.6 m/s b) 12.56 m/sc) 11.2 m/s d) 13.6 m/s

102) If a cyclist doubles his speed whilenegotiating a curve, how does thetendency to overturn vary?a) Remains unchangedb) Doubledc) Halvedd) Ouadrupled

Ans -(93 - c) (94 - b) (95 - c)

(96 - c) (97 - b) (98 - c)

(99 - c) (100 - b) (101 - b)

(102 - d)

23


DNYANSAGARA. Nagar

CIRCULAR MOTION

103) A road is 10 m wide. Its radius ofcurvature is 50 m. The outer edge isabove the lower edge by a distance of 1.5m. This road is most suited for thevelocitya) 2.5 m/s b) 8.57 m/sc) 6.5 m/s d) 3.5 m/s

104) A small body of mass m slides down ahemispherical smooth bowl from therim to the bottom. The velocity of thebody at the bottom is :

a) gr2 b) gr5

c) gr d) None of these.105) A particle moves in a circle of radius 25

cm at two revolutions per second, theaceleration of particle in m/s2 is:a) 2 b) 4 2

c) 8 2 d) 2 2

106) The radius of the circular path ofparticle is doubled but its frequency ofrotation remains unchanged. If theinitial centripetal force be F, then thefinal value of the centripetal force willbe :a) F b) 2Fc) 4F d) F/2

107) A particle P is moving in a circle ofradius ‘a’ with uniform velocity v.C. iscentre of the circle and AB is adiameter.The angular velocity of P about A and Care in the ratio :a) 1 : 1 b) 2 : 1c) 1 : 2 d) 4 : 1

108) A particle of massm is rotating by meansof a string in a vertical circle. Thedifference in the tensions at the bottomand the top would be:

a) 6 mg b) 4 mgc) 2 mg d) 3 mg.

109) A car is moving in a circular horizontaltrack of radius 10 m, with constant speed10 m/s. A bob is suspended from roof ofcar with rod. Angle made by rod withvertical : (g = 9.8 m/s2)a) Zero b) 450

c) 300 d) 600

110) A can filled with water is revolved invertical circle of radius 4 m and waterjust does not fall down at the highestpoint. The time period of revolutionis(g= 9.87 m s-2) :a) 1 sec b) 2secc) 4 sec d) 8 sec

111) A simple pendulum of length 1 m, thebob performs circular motion inhorizontal plane if its string making anangle 600 with the vertical, then theperiod of rotation of the bob will be ( g= 10 m/s2)a) 2 s b) 1.4 sc) 1.98 s d) 4 s

112) 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) Halvedc) Tripled d) Quadrupled

Ans -(103 - b) (104 - a) (105 - b)

(106 - b) (107 - c) (108 - a)

(109 - b) (110 - c) (111 - b)

(112 - d)

24


DNYANSAGARA. Nagar

CIRCULAR MOTION

113) A disc revolves in a horizontal plane atthe rate of 210 r.p.m. A coin placed at adistance of 2cm from the axis of rotationjust remains at rest on the disc. Thecoefficient of friction between the discand coin is (g = 10 m s-2)a) 0.97 b) 0.5c) 0.35 d) 1

114) A person with his hands in his pocket isskating on ice at the rate of 10 m/s anddescribes a circle of radius 50 m. Whatis his inclination to the vertical?(g = 10 m/s2)

a) tan FHGIKJ1 12 b) tanFHGIKJ1 3

5

c) tanFHGIKJ1 15 d) tanFHGIKJ1 1

10

115) A proton revolves round a circular pathof radius 0.1 m. If it is acted upon by aforce 4 x 10-13 N to keep it moving, theangular 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 of72 km/hr on a flat road takes a turn onthe road at a point where the radius ofcurvature of the road is 20 m. In orderto avoid skidding, he must bend w.r.t. thevertical plane by a n angle greaterthan : (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 circulartrack of radius 10 m with a constantspeed 10m/s. If a bob is suspended formthe roof of the car by light rigid rod of

length 1 m, then the angle made by therod with thetrack will be (g = 10 m/s2)a) zero b) 300

c) 450 d) 600

118) The string of a simple pendulum ishorizontal at a given height and isreleased. The tension in the string at thelowest point is :a) T = mg b) T = 2 mgc) T = 3 mg d) T = 4 mg

119) In an atom two electrons move round thenucleus in circular orbits of radii R and4R respectively, the ratio of time takenby them to complete one revolution is :

a)14 b)

81

c)41 d)

18

120) A motor car is travelling at 30 m s-1 ona circular curve of radius 500 m. It isincreasing its speed at the rate of2 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 these121) In a circus a rider rides in a circular

track of radius R in vertical plane. Theminimum velocity at the highest pointof the track is :

a) 2gR b) 3gR

c) 2gR d) gR

Ans -(113 - a) (114 - c) (115 - a)

(116 - c) (117 - c) (118 - c)

(119 - d) (120 - c) (121 - d)

25


DNYANSAGARA. Nagar

CIRCULAR MOTION

122) A train is safely negotiating a curve ofradius 500 m at a speed of 54 m hr-1. Byhow much should the outer rail beraised, if the distance between the tworails is 1.5 m? (g = 10 m s-2)a) 6.75 cm b) 15 cmc) 4.5 cm d) 2.5 cm

123) Kinetic energy of a body moving invertical circle isa) constant at all points on a circleb) different at different points on a

circlec) zero at all the point on a circled) negative at all the points

124) A motor car is travelling at 20 m/s on acircular curve of radius 100 m. It isincreasing its speed at the rate of 5 m/s2

what is its acceleration?a) 2 m/s2 b) 6.4 m/s2

c) 4 m/s2 d) 9 m/s2

125) When a particle is moved in a verticalcirclea) it has constant radial and tangential

accelerationb) it has variable tangential and radial

accelerationc) it has only constant radiual accelerationd) it has only constant tangential

acceleration126) A ball of mass 0.25 kg attached to the end

of a string of length 1.96 m is moving ina horizontal circle. The string willbreak if the tension is more than 25N.what is the maximum speed with whichthe ball can be moved?a) 14 m/s b) 4 m/sc) 3.92 m/s d) 5 m/s

127) A particle of mass 100 g is tied to oneend of string of length 1 m. It rotates ina vertical circle. When the string makes

an angle of 600 with the vertical, itsvelocity is 2 m/s. The tension in thestring in this position : (g = 9.8 m/s2)a) 0.4 N b) 0.89 Nc) 0.09 N d) 0.98 N

128) A weightless thread can support tensionupto 30 N.A. stone of mass 0.5 kg is tiedto it and is revolved in a circular pathof radius 2m in a vertical plane. If g =10 m/s2, then the maximum angularvelocity of the stone will be :a) 5 rad/s b) 30 rad/s

c) 60 rad/s d) 10 rad/s129) A pilot of mass 81 kg loops the loop with

steady speed of 300 km/h. If the radiusis 0.5 km then the force with which thepilot is pressed into the seat at thehighest point of the loop, isa) 3.15 x 102 N b) zeroc) 8.10 x 102 N d) 19.35 x 102 N

130) A mass of 100 g is tied to one end of astring 2 m long. Thebody is revolvingin a horizontal circle making amaximum of 200 rpm. The outer end ofstring is fixed at the centre ofrevolution. The maximum tension thestring can bear is approximately :a) 8.76 N b) 8.94 Nc) 89.42 N d) 87.64 N

Ans -(122 - a) (123 - b) (124 - b)

(125 - b) (126 - a) (127 - b)

(128 - a) (129 - a) (130 - d)

26


DNYANSAGARA. Nagar

CIRCULAR MOTION

131) A stone of mass 16 kg is attached to astring 144 m long and is whirled in ahorizonal circle. The maxmium tensionthe string can stand is 16 newton. Themaximum velocity of revolution that canbe given to the stone without breakingit, will be :a) 20 ms-1 b) 16 ms-1

c) 14 ms-1 d) 12 ms-1

132) Assuming the coefficient of frictionbetween the road and tyres of a car to be0.5 the maximum speed with which thecar can move round the curve of 40 mradius without slipping if the road isunbanked should be : (g = 9.8 m/s2)a) 25 m/s b) 19 m/sc) 14 m/s d) 11 m/s

133) A weightless thread can bear tensionupto 3.7 kg wt. A stone of mass 500g istied to it and revolved in a circular pathof radius 4 m in a vertical plane. If g =10 ms-2, then the maximum angularvelocity of the stone will be :a) 4 rad/s b) 16 rad/sc) 21 d) 2 rad/s

134) A boy on a cycle pedals around a circleof radius 20 m at a speed of 20 m/s. Thecombined mass of boy and the cycle is90 kg. The angle that the cycle makeswith 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 verticalcircle of radius r. Its minimum velocityat the highest point of the circle will be:

a) gr3 b) gr2

c) gr d) 2/gr136) If a body of mass 0.1 kg tied with a string

of length 1 m, is rotated in vertical

circle, then the energy of the body at thehighest position will be (g = 9.8 m/s2)a) 2.45 J b) 1.25 Jc) 3.45 J d) 4.45 J

137) The maximum velocity at the lowestpoint, so that the string just slacks athighest point in a vertical circle ofradius l, is :

a) gl b) gl3

c) gl5 d) gl7

138) The second hand of a watch has length6cm. Speed of end point and magnitudeof difference of velocities at twoperpendicular position will be :a) 6.28 and 0 mm/sb) 8.88 and 4.44 mm/sc) 8.88 and 6.28 mm/sd) 6.28 and 8.88 mm/s

139) A 500 kg car takes round turn of radius50m with a velocity of 36 km/h. Thecentripetal force is :a) 250 N b) 750 Nc) 1000 N d) 1200 N

140) A hollow sphere has radius 6.4 m.Minimum velocity required by motorcyclist at bottom to complete the circlewill be :a) 17.7 m/s b) 12.4 m/sc) 10.2 m/s d) 16.0 m/s

Ans -(131 - d) (132 - c) (133 - a)

(134 - c) (135 - c) (136 - a)

(137 - c) (138 - d) (139 - c)

(140 - a)

27


DNYANSAGARA. Nagar

CIRCULAR MOTION

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

a) 2 b) 21

c) 4 d) 41

142) A body of mass 2 kg attached to a cordand whirled in a vertical circle of radius2 m. The minimum speed at the bottomof the circle so that the cord will notslacken when the body rounds the top ofthe circle will be ( g = 10 m/s2)a) 10 m/s b) 6.3 m/sc) 7 m/s d) 5 m/s

143) When angular velocity of a uniformrotating body has increased thrice, theresultant of forces applied to itincreases by 60 N. Find the accelerationof the body, in two cases if the mass ofthe 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 ofconstant magnitude which is alwaysperpendicular to the velocity of theparticle, the motion of the particle takesplace in a plane. It follows that :a) its velociyt is constantb) in moves in a straight linec) its kinetic energy is constantd) its acceleration is constant

145) The earth (mass = 6 x 1024 kg) revolvesround the sun with angular velocity2 x 10-7 rad/s in circular orbit of radius1.5 x 108 km. The force exerted by sunis:a) 3.6 x 1021 N b) 3.6 x 10-21 N

v

c) 36 x 1021 N d) 3.6 x 109 N146) Two racing cars of massesm1 andm2 are

moving in circles of a radii r1 and r2respectively. Their speeds are such thatthey each make a complete circle in thesame length of time t. The ratio of theangular speed of the first to the secondcar is :a) m1 : m2 b) 1 : 1c) r1 : r2 d) m1r1 : m2r2

147) Breaking tension in the string is 80 N. Abody of mass 0.1 kg is attached to it andwhirled in circle of radius 0.5m. Whatwill be maximum period of revolutionbefore string breaks?

a) s b) s20

c) s5

d) s10

148) A tube of length L is completely filledwith an incompressible liquid of massm and closed at both ends. The tube isthen rotated in horizontal plane aboutone of its end with uniform angularspeed . What is force exerted by liquidat the other end?

a)2

2mLb)

4

2mL

c) 2mL d)8

2mL

Ans -(141 - c) (142 - a) (143 - d)

(144 - c) (145 - c) (146 - a)

(147 - b) (148 - a)

28


DNYANSAGARA. Nagar

CIRCULAR MOTION

149) The maximum speed with which a carcan be safely driven along a curved roadof radius 30 m and banked at 300 withhorizontal :a) 130 m/s b) 14.00 m/sc) 1.303 m/s d) 13.03 m/s

150) Find the maximum velocity foroverturning a car moved on a circulartrack of radius 100m. The coefficient offriction between the road and tyre is 0.2.a) 0.14 m/s b) 140 m/sc) 1.4 km/s d) 14 m/s

151) A coin placed on a rotating table justslips when placed at a distance 4r fromthe centre. On doubling he angularvelocity of the table. The coin will justslip when distance from centre is equalto :a) 4r b) rc) 2r d) r/4

152) A particle of mass m describes a circleof radius r. The centripetal accelerationof the particle is 4/r2. What will be themomentum of the particle?a) 4 m/r b) 2 m/rc) 4 m / r d) 2 m/ r

153) A bucket tied at the end of a 1.6 longstring is whirled in a vertical circlewith constant speed. What should be theminimum speed so that the water fromthe bucket does not spill when the bucketis at the highest position? (Take g = 10m/s2)a) 4 m/sb) 6.25 m/sc) 16 m/sd) None of the above

154) 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

4

kg is blasted upwards with an initialaccleration of 10 m/s2. Then the initialthrust 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 N155) In an atom two electrons moves round

the nucleus in circular orbitsof radii R& 4R respectively the ratio of the timetakan by them to complete onerevolution is:a) 1/4 b) 4/1c) 8/1 d) 1/8

*****

Ans -(149 - d) (150 - d) (151 - b)

(152 - d) (153 - a) (154 - b)

(155 - d)

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Circular Motion ( MCQ )