Circular Motion Questions and Answers

A particle starts moving from rest at t 0 on a circular path of radius R accelerates uniformly for t and covers the distances during this time Find the angle between acceleration at time t and acceleraton at t 0 initial acceleration R R S R S R tan 1 tan 1 2s R 2s R

A pendulum of mass m length I is released when it makes an angle of 60 with the vertical It collides with a block of mass 3m elastically kept at the lowest position of its path The block stops 1 second after the collision coefficient of friction between the block surface is 0 5 Find the length of the string in m 3m m 0 5

5 Force acting on an object moving on a circle depends on its mass speed and radius as F x m v r Find y z

A particle is moving in a circular path of radius R with a constant speed vo If the particle s speed is and the decreased by a factor of i e v Vo B radius of circular path is doubled then the centripetal acceleration decreases by a factor m n The value of mn is

The speed of a body revolving in a vertical circle of radius r at the lowest point is 5gr The tension in the string at the upper most position will be OPTIONS MARK FOR REVIEW CLEAR SELECTION OA mg

A uniform square plate of mass m is supported as shown in the following Fig If the cable suddenly breaks the angular acceleration of the plate is 4g 1 5 2b 3 3g 2 2b BU 2g 2 3 2b 4 min

uniform magnetic field exists in the region The particle traces a Answer A B C Your Attempt Correct answer angular velocity of particle remains constant speed of particle decreases continuously total mechanical energy of the particle remains conserved Rate this ques

To whirl a stone tied to a cord one has to move the free end of the chord on a circular path pulling the stone on a larger circular path In this way a stone of mass m is whirled on a horizontal circular path of radius R with the help of a light inextensible cord of length by moving the free end on a circular path of radius r with a uniform speed v as shown in the figure At sufficient great speed tensile force in cord becomes so large that the effect of gravity can be neglected but at this speed air resistance becomes considerable The force of air resistance is expressed as NR n R given 1 nr F mv Path of the hand Find N R Path c the stor

The voltage across a pure inductor is represented by the following diagram Which one of the following diagrams will represent the current Question Type Single Correct Type 1 2 3 4 MA A n n

A particle is projected over a triangle from one end of its horizontal base to graze the vertex and fall at the other end of the base If B and C are the base angles and a the angle of projection then A sin a sin B sin C B cos a cos B cos C C tan a tan B tan C D cot a cot B cot C

Zero Marks 0 In all other cases Consider two rings with radius r 1 5 m as depicted in the figure the ring 1 is at rest and the ring 2 rotates around the point O which is one of the intersection points of the two rings with a constant angular speed w 2 ad s Find maximum speed in m s of the other intersection point of the two rings 30 Ring 1 Packeroco Ring 2

2 23 A disc is rotating freely about its axis Percentage change in angular velocity of disc if temperature decreases by 20 C is coefficient of linear expansion of material of disc is 5 10 C

A rigid body is rotating at the rate of 3 rads about an axis AB where A and B are the points 1 2 1 and 3 4 2 The velocity of the point P at 5 1 1 of the body is a 3i 8j 10k c 2i 2j k 3 3i 8j 10k 3 d 4i j 2k b

A billiard ball initially at rest is given a sharp blow by a cue stick The impulse is horizontal and is applied at a distance 2R below the centreline as shown in figure The initial speed of the ball is uo and the coefficient of kinetic friction is Hk R POOL L Initially kinetic friction acts in direction Initially kinetic friction in i direction Ball instantaneously starts pure rolling Initial angular velocity of ball is 5v0 38

marks Two bodies A and B are moving with same constant speed v in clockwise direction in a horizontal circle of radius R and are initially dimetrically opposite The particle 8 is now acted by a force giving a tangential acceleration m s Then U they collide after time they collide after time R a 2 R a relative velocity just before collision is aR relative velocity just before collision is 2maR R Ve B Save N

Amusement Park Swing CW An amusement park swing has horizontal wings fixed at the axis of length 2 m and ropes of lengths 2m from the other end of the wing Each rope hold a chair rider of total mass m If the angle made by the rope with the vertical is 37 find the angular speed of the rotation Take g 10 m s I 1

An electric fan has blades of length 30 cm measured from the axis of rotation If the fan is rotating at 120 rpm the acceleration of a point on the tip of the blade is a 1600 m s c 23 7 m s b 47 4 m s d 50 55 m S 1990

An earth satellite of mass m orbits along a circular orbit C at a height 2R from earth s surface It is to be transferred to a circular orbit C2 of bigger radius at a height 5R from earth s surface The transfer is affected by following an elliptical path as shown in figure Calculate the change in the energy required at point B R radius of earth A 5R 2R C C

A particle is moving in x y plane At certain instant the components of its velocity and acceleration are as follows V 3m s Vy 4m s a 4m s a 2m s and 1 m s2 The rate of change of speed at this moment is ay

Consider a simple pendulum of length 1 m Its bob performs a circular motion in horizontal plane with its string making an angle 60 with the vertical The centripetal acceleration experienced by the bob is LA 17 3 m s C 10 m s B 5 8 m s 5 m s D

D Instantaneous and average acceleration are sa Diagram shows three particles A B C Particle B is moving in a circle of radius R with constant angular velocity w clockwise A C are at rest Choose the correct statement s A Angular velocity of B wrt A is a clockwise B Angular velocity of B wrt A is wanticlockwise C Angular velocity of B wrt C is constant equal to w D Angular velocity of B wrt C is not constant and is w A 160 B on angle with

0 19 10 A simple pendulum of length carries a bob of mass m If the breaking strength of string is from the vertical can be 60 30 COST COST 2 3 314 312 2mg the maximum angular a

izontal ground round ling 5 40 A small body of mass m tied to an inextensible thread moves over a smooth horizontal plane The other end of the thread is passed through a hole and drawn with a constant velocity v Find the tension of the thread as the function of the distance r of m from the hole if at r ro the angular velocity of the thread is equal to 0 Ans 2 4 moor 2

0 The coefficient of friction between the rubber tyres and the road way is 0 25 The maximum speed with which a car can be driven round a curve of radius 20 m without skidding is g 9 8 m s a 5 m s b 7 m s 2020 c 10 m s d 14 m s

A small block of mass m is at rest with respect to a smooth hemispherical bowl of radius R rotating with angular velocity w about its axis as shown in figure Find the radius of the circle r over which block is moving as seen from ground Answer A B C Your Attempt V O R WAR g2 w WAR g2 2w r R m Correct answer Rate this questio

A particle moves along a circle of radius T with constant acceleration If the velocity of the particle is 80 m s at the end of second revolution after motion has begun the tangential acceleration is A 40 m s C 640 m s B 40 m s D 160 n m s

Three point particles P Q R move in a circle of radius r with different but constant speeds They start moving at t 0 from their initial positions as shown in the figure The angular velocities in rad sec of P Q and R are 5 m 2 3 respectively in the same sense The time interval after which they all meet is A 2 3 sec B 1 6 sec C 1 2 sec D 3 2 sec 5

Write the velocity of the points shown in figure in vector form if the wheel R 2m undergoes pure rolling with 10rad sec Also Find out the speed of COM of the rigid body B 60 100 309 A

A ball of mass m is hanging from a string of length L which is attached to a L shaped massless rod The rod is fixed on a block which is also of mass m the whole assembly is kept on a horizontal frictionless surface as shown in diagram A bullet of mass m moving in horizontal direction collides head on with the hanging ball inelastically with speed v so that after collision the ball is just able to complete the circle m L m Column I A The value of v is m oble B The value of speed of ball just after collision at the smooth Column II p 13gL q 5gL lowest position of circle C The speed of L shaped rod r 52gL when ball is passing the horizontal position D The speed of the ball with respect to ground at the topmost position 8 8L 2 13 1 3

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution If this particle were projected with the same speed at an angle 0 to the horizontal the maximum height attained by it equals 4R The angle of projection 0 is then given by 1 0 sin 1 2gT2 T R 2 2 3 4 0 cos 0 cos 1 gT2 T R 1 0 sin 1 2R T R gT T R 1 2 2 2 2

A charged particle is projected with velocity vo in combined uniform electric field 2 and uniform magnetic field 8 Column Il gives the possible path particle corresponding to condition in Column 1 Match the entries in Column 1 with entries in Column II Column l 01 E 0 B 0 02 E 0 B 0 Q3 E 0 B 0 04 E 0 B 0 Column II A1 Straight line A2 Parabola A3 Helix A4 Circle

A cyclist riding the bicycle at a speed of 23 14 3 m s takes a turn around a circular road radius 20 3 m without skidding Given g 9 8 m s vertical 1 30 3 45 what is his inclination to the 2 90 4 60 AS ASSA 20 3m Gig avis a g 9 8 m s 1 30 3 45

Two solid splisies vachi of mass M and radius R2 are connected with a rod of mass M connected to their surfaces normally as shown in the figure The moment of inertn of the system about an axis passing through the center of one of the spheres and perpendicular to the rod wil he center to center distance of the spheres i 2R M RIZ 317 60 2R 2 M R12 MR

ings of equaller rotates so that the ball moves in a circle with each string making an angle 53 with vertical If the period of the ball s circular motion is 2 sec Find tension in each string sin 53 0 8 10 53 I

Sir mam plz explain the answer 11 In uniform circular motion NCERT Pg 80 1 Acceleration of the particle changes continuously 2 Acceleration of the particle remains constant 3 Velocity of the particle remains constant 4 Speed of the portiola change continuously

A body of mass 100 g is revolving in a horizontal circle If its frequency of rotation is 3 5 r p s and radius of circular path is 0 5 m the angular speed of the body is A 18 rad s B G 22 rad s D 20 rad s 24 rad s

Circular Motion 60 3 A disc is rotating with constant angular velocity about an axis passing through centre C and perpendicular to the plane of disc An insect is moving over the disc along radial direction with constant velocity with respect to the disc Acceleration of the insect at the instant when its distance from centre is r will be A re towards the centre B ro away from the centre C Less than ro in magnitude D Greater than ro in magnitude

One end of an ideal string is connected with a point mass of mass m and the other end is connected with a fixed point O A ball can move in vertical circle At the lowest point speed of ball is v Line connecting B D O is horizontal A is lowest point and C is highest point of circle OIS 11 PU III T IV P 1 III IV List l v ge v 2g v 3g v 4ge B List II P Speed at B is ge Q Speed at B is 2g R Speed at B is zero S Particle completes circular motion T Particle does not complete circular motion U Data insufficient

An insect trapped in a circular groove of radius 7 cm moves along the groove steadily and completes 5 revolutions in 200 s What is the linear speed of the motion 1 1 1 cm s 3 4 4 cm s 2 2 2 cm s 4 none of these

Suppose a spring with spring constant 7 N m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass Suppose that the friction of the mass with the floor i e the damping constant is 5 N s m a Set up a differential equation that describes the system b is the system over damped critically damped or under damped

25 A rod of mass m and length L m is hinged in a plank of same mass m The plank is kept on a 6 smooth horizontal surface and rod makes angle 0 with the vertical The system is released from re from 0 0 The velocity in m s of the plank when the angle 180 is Take g 10 m s 5

mass attached to one end of a string crosses top most point on a vertical circle with critica Deed Its centripetal acceleration when string becomes horizontal will be g gravitationa cceleration B 3g C 4g D 6g

A particle is performing a uniform circular motion along the circumference of a circle of radius R and T is the periodic time In the time T 4 its displacement and distance covered are respectively C 2R TR D 2R TR A VZR TR 4 B TR 2 VZR 2

Q 1 MULTIPLE CHOICE A straight track is tangent to a circular track of radius R Two particles A and B start simultaneously at t 0 from the common point P of the track The particle A moves with uniform velocity u on the straight track whereas the particle B moves on the circular track always keeping itself collinear with the center of the circular track and the particle A as shown in figure Ich 4 RAvui qu qy qz zuef zum 31 344A8 fa P t 0 B u HY TA GR GRIH GR 1 Hu A 94 92 A f ga Gdfch cu B za ch ata faa zey xjuz qau q4 h au u A mu za tu amy zu gy qau 94 92 na P A is w t w t Angular speed of B as function of time t uR R u t w t uR 2 R u t Correct Answer B is w t B Angular speed of B as function of time t 2uR R u t 2uR R u t Bunu d B C Magnitude of acceleration of particle B when it is at angular position 0 is R cos 0 1 3sin 0 R ja gu Bhufu fa 8 42 a suh azu chi cos 0 1 3sin 0 u R Correct Answer D when it is at angular position 8 is 2 2R 3 cos 0 1 3sin 0 una Magnitude of acceleration of particle B facc

Two resistance of 100 and 200 and an ideal inductor of inductance 5H are connected to a 20 V battery through a key K as shown in figure The key is closed at t 0 What is the final value of current in the 100 resistor 20V 100 www moooo SH K 1 A 2002 www

A particle is moving in a circle has initial angula velocity 50 rpm and has an angular acceleration d rad s2 Its angular velocity after one minute is 2 850 rpm 4 None of these 1 110 rpm 1850 rpm

Angular acceleration a of a body is given by the 4at3 3bt If initial angular velocity of relation a the body is wo then its angular velocity at time t will be Law att bt 2 4at 3bt 3 12at 6bt 14 h 3

A mass m moves in a circle plane with velocity v in a circule of radius R The mass is attached to a string which passes through a smooth hole in the plane as shown The tension in the string is increased gradually and R R slowly and finally m moves in a circle of radius The final value of kinetic energy is 1 mv 2 1 3 mv 2 mv 4 2mv 2

A car is moving at a speed of 72 km hr The diameter of its wheel is 0 5 m If the wheels are stopped in 20 rotations applying brakes then angular retardation produced by the brakes would be rad a 45 5 rad s rad b 33 5 2 2 S c 25 48 2 s 0 9 rad S d 50 9

A car is moving with a speed of 30 m sec on a circular path of radius 500 m Its speed is increasing at the rate of 2m2 The acceleration of the car is a 9 8 m 2 b 1 8 m 2 A 2 7 11 2 c 2 m 2 S