Circular Motion Questions and Answers

2 29 A point P is located on the rim of wheel of radius r 0 5 m which rolls without slipping along a horizontal surface then the total distance traversed by the point P in meters between two successive moments it touches the surface is m

There is a parabolic shaped bridge across a river of width 100 m The highest point of the bridge is 5 m above the level of the banks A car of mass 1000 kg is crossing the bridge at a constant speed of 20 ms 1 m Using the notation indicated in the figure find the force exerted on the bridge by the car when it is at the highest point of the bridge Ignore air resistance and take g as 10 ms A 6 4 KN C 8 4 KN B 7 2 KN D 9 2 KN

A particle performing uniform circular motion has angular momentum L If its angular frequency is doubled and its kinetic energy halved then the new angular momentum is 1 L 4 3 4L 2 2L 2003 4 L 2

10 The figure shows a frictionless horizontal track which smoothly turns into a frictionless inclined surface of inclination 0 A ring of radius R rolling without slipping on the horizontal surface with angular speed moves towards the inclined surface The maximum distance along the incline plane moved by the ring is 1 R 2g 00R Co 2 R 2g sin e

3 The maximum acceleration of a particle in SHM is made two times keeping the maximum speed to be constant It is possible when a amplitude of oscillation is doubled while frequency remains constant b amplitude is doubled while frequency is halved c frequency is doubled while amplitude is halved d frequency of oscillation is doubled while amplitude remains constant otion

A rod is hinged by one end in the horizontal plane in the absence of gravity A small bead of mass m is inserted on the rod at L length from the hinged end The coefficient of friction between the bead and the surface of the rod is u The rod starts moving with constant angular acceleration a rad s Find out the time when the bead starts slipping a rad s L

If the equation for the displacement of a particle moving on a circular path is given by 8 2t 0 5 where 8 is in radian and t is in second then the angular velocity of the particle at t 2s is A O 26 rad s B O 12 rad s C O 8 rad s D O 24 rad s

A small body of mass m slides down from the top of hemisphere of radius r The surface of block and hemisphere are frictionless The height at which the body lose contact with the surface of the sphere is uestion Type Single Correct Type 1 2 1 2 h r 13 h

A bucket tied at the end of a 1 6 m 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 sec uestion Type Single Correct Type 1 2 3 4 m sec 6 25 m sec 16 m sec C

For the given situation particle will For vertical circular motion 1 estion Type Single Correct Type 2 R 1m 3 U 20 m s Leave the circular path Perform circular motion Oscillate in lower half circle

A stone of mass 0 25 kg tied to the end of a string is whirled round in a circle of radius 1 5 m in a horizontal plane What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N uestion Type Single Correct Type 1 2 3 30 m s 35 m s 40 m s 60 m o

40 An insect crawls up a hemispherical surface very slowly see fig The coefficient of friction between the insect and the surface is 1 3 If the line joining the center of the hemispherical surface to the insect makes an angle a with the vertical the maximum possible value of a is given by

11 Let escape velocity of a body kept at surface of a planet is u If it is projected at a speed of 200 more t the escape speed then its speed in interstellar space will be 1 u 3 211 2 4 3 u 25

particle moves along a circle of rad us r with constant tangential acceleration If the velocity f the particle is v at the end of second revolution after the revolution has started then the ngential acceleration is A 8 r B 6 r C 4 r D 2 r

body of mass m is performing a U C M in a circle of radius r 2 ne by the centripetal force in moving it through r 3 my r B 2mmy r C zero rd of the circular path is D 2mv 3

A ball weighting 16 N is attached to a central shaft of a grinding machine and a rod which can take a maximum force of 3 KN If the arm of rotating rock is 100mm determine the maximum speed of the ball in revolution in minule rpm which can the safely permitted 15 45

LAR MOTION Two racing cars of masses m and m are moving in circles of radii r and r respectively Their speeds are such that each makes a complete circle in the same time t The ratio of the angular speeds of the first to the second car is a c 1 1 b m m d m m Fr

The real force F acting on a particle of mass m performing circular motion acts along t radius of circle r and is directed towards the centre of circle The square root of magnitude such force is t periodic time T mr B ATT 2n A 2 mr C 2 T mr D Tmr 4T

stone of mass 1 kg is tied to a string 2 m long and is rotated at constant speed of 40 ms ns ertical circle The ratio of the tension at the top and the bottom is Take g 10 ms A 12 10 B 79 C 21 D 81 79

A bit of mud stuck to a bicycle s front wheel of radius R detaches and is flung horizontally forward when it is at the top of the wheel The bicycle is moving forward at a speed v and it is rolling without slipping The horizontal distance travelled by the mud after detaching from the wheel is A 2rv g B 8rv g C 4rv g D 16Rv g

article is moving in a vertical circle with radius 1 m If the ratio of s tension Find the velocity of particle at highest point LO HER Till 25th Feb 2021 shift 1 A 5 m s

5 Assertion A particle in xy plane is governed by x a sin at and y a cos at where a as well as w are constants then the particle will have parabolic motion Reason A particle under the influence of mutually perpendicular velocities has curvilinear motion 1

Two particles having the same specific charge enter a uniform magnetic field with the same speed but at angles of 30 and 60 with the field Let a band cbe the ratios of their pitches radii and periods of their helical paths respectively then gaand aan de la OPTIONS MARK FOR REVIEW CLEAR SELECTION A abc 1 B a b 2 60 god com a sad gusta e C a c 197

3 20 66 rad s2 13 A cord of negligible mass is wrapped around a solid cylinder of a mass 20 kg and radius 20 cm A steady pull of 25 N is applied on cord tangentially The cylinder is mounted on horizontal axis with frictionless bearings What is kinetic energy of wheel when 2 m cord is unwound NCERT Pg 171 1 50 J 2 100 J 3 150 J 4 90 J so that its COM has speed work required to stop it is 1 2 J 2 3J 3943 4 8 J 17 To maintain a rotor at a speed of 200 rad s an transmit a torque of 125 N required by the engine 1 15 kW 2 3 25 kW

A particle is projected from ground with speed u at an angle with the horizontal Radius of curvature is minimum at the highest point is minimum at the point of projection is same at all the points cos

Two small balls A B of masses m and 2m respectively are connected by an ideal thread of length I are kept on a smooth horizontal surface as shown The ball B is given sudden vertical velocity u as shown Ball B acquires a speed v when thread becomes vertical for the first time Acceleration due to gravity is g The value of u is such that ball A is on the verge of lifting off floor when thread is vertical Mark the INCORRECT option s 2m B a The acceleration of B at the instant when its speed is v is 3g 2 b The value of u is 3gl c The value of v is gl d The radius of curvature of path of B when its speed is y is

7 Block A of weight 200 N connected to block B of weight w using a rope that passes over a fixed cylinder as shown in figure Determine minimum weight of block B for which no motion occurs Assume coefficient of static friction between the rope and the cylinder as 0 2 and between the block A and horizontal surface as 0 3 LLL A 140 N

A uniform disc of mass M 2 50 kg and 12 radius R 0 20 m is mounted on an axle supoorted on fixed frictionless bearings A light cord wrapped around the rim is pulled with a force 5N On the same system of pulley and string instead of pulling it down a body of weight 5 N is suspended If the first process is termed A and the second B the tangential acceleration of point P will be M 5N Pull M mg 5N A B A equal in the processes A and B B greater in process A than in B C greater in process B than in A D independent of the two processes

The free end of the string wound on the surface of a solid cylinder of mass M 1kg radius R 2 m mis pulled up by a force F as shown If there is sufficient friction between cylinder floor then the upper limit to the angular acceleration in rad s2 of the cylinder for which it rolls without slipping is g 10m s F

2 A rod AB is moving on a fixed constant velocity y as shown in figure P is the point of intersection of the rod and the circle At an instant the from centre of the circle The 3R rod is at a distance x 15 DI velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD P Lear B a Find the speed of point of intersection P b Find the angular speed of point of intersection P with

uration s duration 3 78 A heavy particle of mass m is in motion on a smooth surface of a hemisphere of radius R and there is no friction At the initial instant the particle is at the topmost point A and has an initial velocity vo At what point will the particle leave the surface of the hemisphere Also determine the value of vo for which the particle will leave the sphere at the initial instant 2

3 47 A particle of mass 9 kg is moving under the action of a central force whose potential energy is given by U 10 r For what energy it will orbit a circle of radius 10 m Calculate the time period of this motion Ans 0 5 J 60 sec TC

3 49 A particle A moves along a circle of radius R 50 cm so that its radius vector v relative to the point O rotates with constant angular velocity 0 4 rad s Find its total acceleration Ans 0 32 m s

fa For he a a e 1 S 3 52 A small objects slides without friction from the height 50 cm shown in figure 3 126 and then loops the vertical loop of radius 20 cm from which a symmetrical section of angle 2a has been removed Find the angle a such that after losing constant at A and flying through the air the object will reach at point B Ans 60 H Figure 3 126 2

f the body is moving in a circle of radius r with a constant speed v Its angular velocity is A v r B VT D r v C v r A car of mass 1500 kg is moving with a speed of 12 5 ms on a circular path of radius 20 m o level road What should be the coefficient of friction between the car and the road so that the ar does not slip A 0 2 B 0 4 C 0 6 D 0 8

19 In the setup shown the pulleys the cords and the spring are ideal and masses of the loads are indicated in the figure Initially the system is in equilibrium What should be the range of mass M so that acceleration of the load of mass 2m becomes greater than acceleration of free fall immediately after the cord is cut at point P 20 a M 4m c M 8m WI 11 b M 6m d M 14m

uestion For the given situation find tension T at point P in string Particle is mo ing in vertical circular motion R Im 10m s For the given situation find tension T at point P in string Particle is moving in vertical circular motion Type Single Correct Type 50 N Im 10m s 1 kg

1 40 A particle moves along an arc of a circle of radius R according to the law 1 a sin ot where I is the displacement from the initial position measured along the arc and a and w are constants Assum ing R 1 00 m a 0 80 m and w 2 00 rad s find a the magnitude of the total acceleration of the particle at the points 1 0 and 1 a b the minimum value of the total acceleration wmin and the cor responding displacement m

Vectors Q 13 A particle is moving on a circular path of radius with uniform velocity v The change in velocity when the particle moves from P to Qis ZPOQ 40 P A 2v cos 40 B 2vsin 40 D 2v cos 20 C 2vsin 20 14 If the resultant of A and B makes angle a with A and B with B then 0 V Q

12 A circular race track of radius 300 m is banked at an angle of 15 If the coefficient of friction between wheels and road is 0 25 the optimum speed of the race car is tan 15 0 26 1 24 3 m s 1 2 27 9 m s 1 3 32 6 m s 1 4 38 1 m s 1

On a smooth horizontal surface we have a point charge attached to the free end of a massless rod hinged at other end as shown We apply a uniform electric field E and slightly deflect the rod The force on charge accelerate it during half rotation then the direction of electric field is suddenly reversed so that the charge remain accelerating assuming q 1C m 1kg E 1N C length of rod L 1m The total angle rotated when the point charge attains a speed of 5 m s is 38 n n Then value of n is E q m hinge A

A particle of mass 1kg is suspended from a string of length 2 m from point O as shown Choose the CORRECT statement s for different value of u L u A For u 10 m s particle will complete the vertical circular motion B For u 7 m s particle will deflect more than 90 with vertical C For u 12 m s the maximum height reached by particle will be 5m D For u 20 m s the minimum tension in string will be 150 N during sub sequent motion

c Lonly A bicycle is travelling northwards and so its angular momentum points towards west In what direction should the cyclist apply a torque to turn left a West fe East The principle of conservation of angular momentum states b South d North made x n LAYO c wx n 2 3 305A uniform rod smooth horizon end B perpen

Leys A cyclist taking turn bends inwards while a car passenger take the same turn is thrown outwards The reason is A car is hear then cycle B has four wheels while cycle has only two C Difference in the speed of the two D Cyclist has to counteract the centrifugal force while in the case of car only the passenger is thrown by this force fa com

C Half way down etphysicots com eshaded nesha one of the above CO A particle of mass m is fixed to one end of a light rigid rod of length 1 If the particle is released from rest at its highest position then the length tension in the rod A is zero when it is vertical B is zero when it is horizontal C is zero when it is making an angle of cos 1 2 3 with the vertical D Cannot be zero in any position Votas

6 A stone of mass 2 kg tie with the length 2 m and moves in vertical circular motion The difference between tension in the thread at lower point and at the highest point is Take g 10 m s NCERT Pg 12 1 60 N 3 30 N 2 120 N 4 240 N

A stone hanging from a massless string of length 15 m is projected Horizontally with speed 147 m s Then the speed of the particle at the point where tension in string equals the weight of particle is A 10 m s B 7 m s D None of these gmail C 12 m s deck 393

4pt 0 a fly wheel is rotating at 50 rpm A motor gives it a constant angular neetphyceleration of 0 5 rad s2 until it reaches 100 rpm The motor is then disconnected How many revolutions are completed at t 20 s A 25 rev B 29 rev C 20 rev D 15 rev

A body of mass 1 kg starts moving from rest at t 0 in a circular path of radius 2 m The power acting on it due to all forces varies as shown in graph Then find the net acceleration in m s of particle at t 2 sec P4 watt

3 Executes SHM 4 Falls freely under gravity 7 Restoring force on the bob of a simple pendulum of mass 100gm when its amplitude is 1 is 1 0 017 N 2 1 7 N 3 0 17 N 4 0 034 N 3 4 The acceleration due to