Circular Motion Questions and Answers

5 A simple pendulum is constructed by attaching a bob of mass m to a string of length L fixed at its upper end The bob oscillates in a vertical circle It is found that the speed of the bob is v when the string makes an angle e with the vertical Find the tension in the string at this instant

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities 01 and 02 They are brought into contact face to face coinciding the axis of rotation The expression for loss of energy during this process is 1 1 01 002 3 01 0 8 2 1 01 02 4 1 0

For a particle in uniform circular motion the acceleration a at a point P R 0 on the circle of radius R is Here 0 is measured from the x axis 1 2 3 4 R i cos0i sin 0j R R R R sin 0i V cosei cos Oj R sin Oj

44 A car is moving at a speed of 40 m s on a circular track of radius 400 m This speed is increasing at the rate of 3 m s2 The acceleration of car is 1 4 m s 2 7 m s2 3 5 m s

the following option is not correct for inelastic collision The velocity of both the particles may be same after the collision 2 Kinetic energy is not conserved 3 Linear momentum of the system is conserved Velocity of seperation may be greater than velocity of approach

3 6 5 A man of 50 kg mass is standing in a gr space at a height of 10 m above the floor H throws a stone of 0 5 kg mass downwards with speed 2 m s When the stone reaches the flo the distance of the man above the floor will be 1 20 m 3 10 1 m kg Best 2 9 9 m 4 10 m JON C

A particle P is moving in a circle of radius r with uniform speed v C is the centre of the circle and AB is diameter The angular velocity of P about A and C is in the ratio 1 4 1 3 1 2 2 2 1 4 1 1

A body of mass 1 kg is moving in a vertica circular path of radius 1 m The differenc between the kinetic energies at its highest an lowest position is 1 20 J FI 2 10 J 4 106 5 1 J

A particle has initial velocity V i j and a constant force F i j acts on the particle The path of the particle is 1 straight line 3 circular 2 parabolic 4 elliptical

which of the coins will revolve with the 38 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 Explain clearly why the motorcyclist does not drop down when he is at the uppermost point with no support from below What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m

Choose the incorrect statement about areal velocity 1 Direction of areal velocity is perpendicular to velocity and in the direction of radius vector 2 Direction of areal velocity is perpendicular to both velocity and radius vector 3 Direction of areal velocity is in the direction of velocity 4 Direction of areal velocity is in the direction of radius vector

3 A coin is placed on the horizontal surface of a rotating disc The distance of the coin from the axis is Im and coefficient of friction is 0 5 If the disc starts from rest and is given an angular rad sec the number of 1 acceleration 2 revolutions through which the disc turns before the coin slips is 1 4 TC 2 7 4t 3 5 4 4 3 4

Two identical blocks each of mass m are shown in figure Force exerted by clamp on the pulley is 3 3 mg 4 3 3 mg 4 30 2 3 mg A mg 4

Two wheels having radii in the ratio 1 3 are connected by a common belt If the smaller wheel is accelerated from rest at a rate 1 5 rad s for 10s the angular velocity of bigger wheel will be 1 5 rad s 1 2 15 rad s 1 3 45 rad s 1 4 None of these Current I flows around the wire frame along the

XXX A block of mass m placed on a horizontal conveyor belt is attached at None end of a spring of force constant k The other end of the spring is attached to a support A Coefficients of static and kinetic friction between the belt and the block are s and k sk Initially the belt the block and the support all are moving towards the right with constant velocity u and the spring is relaxed The support is suddenly stopped a Explain qualitatively the mechanism of motion of the block after the support is stopped b Find the maximum and minimum deformations of the spring c Find period T of the oscillatory motion of the block g T 2 x ks kk 1 tant A MK 9 2 MS MK g ANSWERS A xamin k 12 60 x 1 14 15mg 2 2 Enerzy b w mg 2 x m Remix kxmax 2 14 mg x max 2 mg x lex mu 2 1xmax Mk mg CMS MR mg Muz R

25 A particle of mass 10g moves along a circle of radius 6 4 cm with a constant tangential acceleration What is the magnitude of this acceleration if the kinetic en ergy of the particle becomes equal to 8 10 J by the end of the second revolution after the beginning of the motion 1 0 18 m s 3 0 1 m s 2 0 2 m s 4 0 15 m s

A particle of mass m is kept on a smooth cube of mass M and side L as shown in figure Cube start moving with a constant velocity v Displacement of the center of mass along the horizontal direction when particle hit the ground is 2L g 2L g A C mv L m M v Mv L m M v B D 2L m ML V g mv Mv V 2L m ML V q M m smooth

A boy whirls a stone of small mass in a horizontal circle of radius 1 5 m and at height 2 9 m above level ground The string breaks and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of 10 m What is the magnitude of the centripetal acceleration of the stone while in circular motion

3 2 224 A car is moving on a circular track at a speed of 20 m s having radius 100 m If it starts decelerating uniformly at the rate of 3 m s2 the angle made by the resultant acceleration with the direction of its instantaneous velocity is 1 37 3 53 2 127 4 143 230

13 A cylindrical wire of radius R is carrying current i uniformly distributed over its cross section If a circular loop of radius r is taken as amperian loop then the variation value of B de over this loop with radius r of loop will be best represented by 1 f5 di fo di R 2 B de 4 B de R 1

EX Two strings of length 0 5 m each are connected to a block of mass m 2 kg at one end and their ends are attached to the point A and B 0 5 m apart on a vertical pole which T rotates with a constant angular velocity of tension in the upper string T and the lower string T Use g 9 8 m s 7 rad sec Find the ratio T 0 m 0 5 0 5 0 5 ic in moto

with macroscopic i e large When a glass rod is rubbed with a silk cloth charges appear both A similar phenomenon is observed with many other pair bodies Explain how this observation is consistent with the lat conservation of charge

A particle is suspended vertically from a point O by an inextensible massless string of length L A vertical line AB is at a distance L 8 from O as shown The object given a horizontal velocity u At some point its motion ceases to be circular and eventually the object passes through the line AB At the JEE 99 instant of crossing AB its velocity is horizontal Find u L L 8 u

A smooth table is placed horizontally and a spring of unstreched length and force constant k has one end fixed to its centre To the other end of the spring is attached a mass m which is making n revolutions per second around the centre Tension in the spring will be A 47 m k n2 k 4 m n B 4 m k n k 4 m n C 2 m kln k 4 m n D 2 m kn k 4 m n

A light ray is incident perpendicularly to one face to a 90 prism and is totally internally reflected at the glass air interface If the angle of reflection is 45 we conclude that the refractive index n is AIEEE 2004 H 45 45

184 A particle is moving along a circular path of cale a with constant angular velocity w Magnitud displacement of the particle as a function of t is ytbals 1 a cosot to omil edt 16 ot of S 2 acos Vieunul 2 si lainosi imelo A wot

A cylindrical tube of cross sectional area A has two air tight frictionless pistons at its two ends The pistons are tied with a straight two ends The pistons are tied with a straight piece of metallic wire The tube contains a gas at atmospheric pressure P and temperature T If temperature of the gas is doubled then the tension inthe wire is Pressure outside cylinder P 0 To 2PO 2 1 4 PA 3 P A A A 2 P A 2 4 2P A PO 2 Po 2To

26 A swimmer can swim in still water at a speed of 5 m s and takes t and to time to cross a river in shortest time and shortest path respectively If the speed of river increases then time taken to cross the river in shortest time and shortest path be and to respectively Then ES 0 OSS 1 4 t t 1 2 t t t 1 000 8 to spns ne pri am 4 t t t to 3 t t to sta t

80 A point is moving on X Y plane such that y co ordinates varies with time as x a sin wt y a 1 cos wt where a and w are positive constants Velocity of the particle is mie a 1 aw 2 2 aw 3 810 3 aw 4

3 53 225 An object is moving on a circular path of with constant speed v The average acceleration of the object after it has travelled three and half rounds is to adi 1 3 2v Tur 4v 7 ont 9 2 4 4v 3 r moos8 E 2v 7 fr

12 A spot light source is fixed 4 m from the vertical wall and is rotating at rate 1 rad s The spot image moves horizontally on the wall The speed of the spot on the wall when spot light makes angle of 45 with the wall is The line joining spot source and image is in horizontal plane 1 2 m s 2 3 m s 3 8 m s 4 1 m s 217 If u to bo

One end of a uniform rod of mass m and length is clamped The rod lies on a smooth horizontal surface and rotates on it about the clamped end at a uniform angular velocity w The force exerted by the clamp on the rod has a horizontal component 1 mo 2 zero 3 mg 1 TH mo l 2

The tangential component of acceleration of a particle in circular motion is due CO Speed of particle Change in the direction Change in magnitude of velocity min se Rate of change of acceleration

5 Figure shows a block of mass m moving without friction along three tracks with same speed v Normal reaction R R and R relates as m TR TH R R R R R3 2 R R R do D

01 Which of the following is correct 1 It is possible to have dv 0 but dv dt dt 2 It is possible to have 3 It is possible to have X4 All of these dv dt dv dt 0 and d v 0 0 and d v dt d v dt 0 0 ra pra

A mass M attached to a horizontal spring executes S H M of amplitude A When the mass M passes through its mean position then a smaller mass m is placed over is it and both of them move together with amplitude A The ratio of A B M m M D M M m M m C 2 2 M

A satellite can be in a geostationary orbit around earth at a distance r from the centre If the angular velocity of earth about its axis doubles a satellite can now be in a geostationary orbit around earth if its distance from the center is 0 1 7 2 NI r 2 2 2 r 3 4 4 r 2 1 3

What is the refractive index of material of plano convex lens If radius of curvature of the convex surface is 20 cm and focal length of the lens is 30 cm C w c Read More 5

A body performs S H M due to force F with time period 0 8 s If force is changed to F it executes S H M with time period 0 6 s Now both the forces act simultaneously in the same direction on the same body New periodic time is A B C 0 48 s 0 24 s 0 12 s

The bob of a 0 2 m long pendulum describes an arc of circle in a vertical plan f the tension in cord is 3 times the weight of the bob when cord makes an angle of 30 to the vertical then acceleration of bob in that position is O g 2 O 3g 2 Read More g 4

3 y t 4 sin nt 2 y projection of the raidus vecotr of rotating particle P is 1 y t 3 cos It 2 5 where y in m P t 0 where y in m 3m T 4s X 2 y t 3 cos 2nt where y in m 4 y t 3 cos 3 t 2 where y in m NEET 20

A cyclist is riding at speed of 10 m s takes a turn on a horizontal circular road radius 103 m without skidding What is his angle of inclination to the vertical 15 30 45 60

A wheel initially at rest is rotated with uniform angular acceleration The wheel rotates through angle 0 in first 10 seconds and through additional angle of 02 in next 10 seconds The ratio 33 is 04 1 3 1 4 3

wo bodies have their moments of inertia I and 21 respectively about their axes of rotation I Leir kinetic energies of rotation are equal their angular momenta will be in the ratio A 1 2 B 1 2 2 C 2 1 D 1

The ends of the two rods of different materials with their thermal conductivities radii of cross section and lengths in the ratio 1 2 are maintained at the same temperature difference If the rate of flow of heat in the larger rod is 4 cal sec that in the shorter rod will be in cal sec 1 1 2 2 3 8 4 16 d no rhown in figure a 20 cal of heat flows through it in 4

A proton of mass 1 67 x 10 27 kg and charge 1 0 x 10 19 C is projected with a speed of 2 x 106 m s 1 at an angle of 60 to the x axis If a uniform magnetic field of 0 104 T is applied along y axis the path of proton is helix with circular radius 0 2 m radius 0 1 m radius 0 5 m radius 0 7 m

A resistor R and 2uF capacitor in series is connected through a switch to 200 V direct supply Across the capacitor is a neon bulb that lights up at 120 V Calculate the value of R to make the bulb light up 5s after the switch has been closed log 2 5 0 4 AIEEE 2011 1 1 3 10 22 2 1 7 x 10 2 3 2 7 x 10 2 4 3 3 10 rce of voltage 6V is used in an experiment on

A circular hole of radius R 2 is cut from a circular disc of radius R The disc lies in the xy plane and its centre coincides with the origin If the remaining mass of the disc is M then a determine the initial mass of the disc and b determine its moment of inertia about the z axis R y

Q7 Two points A and B are on a disk that rotates about an axis Point A is three times as far from the axis as point B If the speed of point B is v then what is the speed of point A a v b 9v c v 3 d 3v e 3 v

If the perpendicular distance between the point application of force and the axis of rotaion is infinity Select one a No rotation unless the contact is being broken O b The rotation is not possible O c The force applied will be very much high for even a small rotation Od The rotation is possible but the moment generated is very less