Circular Motion Questions and Answers

is true conserved in n never take oes not vary for observers tes c Area and gravitational potential d Impulse and pressure 7 In a two dimensional motion instantaneous speed 1 is a positive constant Then which of the following are necessarily true a The average velocity is not zero at any time b Average acceleration must always vanish c Displacements in equal time intervals are equal d Equal path lengths are traversed in equal intervals

If a car is moving in a circular path with uniform speed then which of the following statement is incorrect It can move with uniform speed 1 but its momentum will keep on changing 2 3 Its speed and momentum both remain uniform throughout the motion It can move with uniform speed but its velocity will keep on changing

23 If an object is moving on a curved path then which of the following physical quantities may be constant during the motion Symbols have usual meanings d 1 v dt 3 TC 2 V 4 Both 1 8 3

d not related to each other 8 For a particle performing uniform circular motion choose the incorrect statement from the following a Magnitude of particle velocity speed remains constant b Particle velocity remains directed perpendicular to radius vector c Direction of acceleration keeps changing as particle moves d Magnitude of acceleration does not remain constant 79 Which of the following statements is incorrect

a 16 ms c 12 m s b 4 ms d 8 ms 84 A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in figure If he maintains constant speed of 10 ms what is his acceleration at point R a 10 m 2 c 0 01 ms b 0 1 ms 2 d 1 ms2 b c d 91 If u them a

A particle starting from rest moves in a circle of radius r It attains a velocity of Vo m s in the nth round Its angular acceleration will be 1 2 3 v 4nr 4knr Vo rad 3 v rad 82 rad s2 rad s

c 85 An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s The linear speed of 92 If t the insect is vals a 4 3 cm s c 6 3 cm s b 5 3 cm s d 7 3 cm s a c

2 5 A particle moving on the inside of a smooth sphere of radius r describing a horizontal circle at a distance r 2 below the centre of the sphere What is its speed A 5gr B 4gr 3 D 3gr 3gr 2

A rider on a motorcycle that has a mass of 195 kg travels with a speed of 25 m s Each of the two wheels of the motorcycle has a radius of 4 m and a moment of inertia of 17 kg m What is the approximate total rotational kinetic energy 3 of the wheels From u answer to 2 decimal places

B1 A cyclist starts from the centre O of a circular park of radius 1 km reaches the edge P of the park then cycles along the circumference and returns to the centre along QO as shown in the figure If the round trip takes ten minutes the net displacement and average speed of the cyclist in metre and kilometre per hour is R 4 0 a 0 1 c 21 4 4 2 d 0 21 4 8 83

An electron of mass me and charge e e 0 moves in a closed orbit in a uniform magnetic field acting perpendicular to the plane of the orbit If Bohr s quantization rule for angular momentum were t be applied to this system the minimum magnetic flux passing through the orbit equals 3 A zero D none of the above B h 2e C h

83 A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed 90 If the stone makes 14 revolutions in 22 s then the acceleration of the stone is a 16 m s c 12 m s 84 A cyclist starts from centre b 4 ms d 8 ms of a

8 A cone filled with a liquid is revolved in a vertical circle of radius 4 m What must be maximum period of revolution if liquid does not fall down 1 3 s 3 5 s 2 4 s 4 6 s 9 When a ceiling fan is switched off its angular velocity falls to half while making 6 rotations How many more rotations will it make before coming to rest Take uniform angular retardation 1 4 3 2 2 3 4 1

5 Two small spheres of equal masses are attached to a string of length 2 m as shown in figure The string and spheres are whirled in a horizontal circle about point O at constant angular speed The ratio of tension is T T 1 1 2 3 1 3 O T m 1 m T 1 m 2 2 3 4 3 2 m

12 02 is 1 A wheel is subjected to uniform angular acceleration about its axis Initially its angular velocity is zero In the first 2 s it rotates through an angle 0 in the next 01 2 s it rotates through an angle 02 The ratio of b 2 a 1 c 3 d 5 ir rotating about its axis with

Three identical particles are joined together by a thread as shown in figure All the three particles are moving in a horizontal plane If the velocity of the outermost particle is vo then the ratio of tensions in the three sections of the string is 0 1 3 5 7 2 3 4 5 3 7 11 6 4 3 5 6 A B l

SolveLancer Test Which of the following is incorrect 1 The dot product of a and for a body in circular motion is always non zero II In circular motion if speed increases the angle between and is obtuse III In circular motion if speed increases the angle between a and is acute IV In circular motion if tangential force is zero then angular momentum of body re constant SolveLancer Test a I II IV b II III I EL FI

A rabbit runs across a parking lot The path is such that components of rabbit s position with respect to an origin of co ordinates as function of time are x 1 10 and y 9t 5 Here x y are in meter and t in second The magnitude of rabbit s displacement during first 5 seconds is 70 5 m 51 5 m 62 5 m 65 5 m

A plank of mass M and length L is hinged at its mid point from a fixed support in vertical plane as shown Plank is free to rotate in vertical plane about the hinge Two persons of equal mass running on the plank with same speed v relative to the plank so that angular velocity of the plank remains constant Assuming they run till running is possible then v is A a constant B independent of the separation between the persons C independent of the distance of the persons from the hinge D independent of their mass Hin

9 A ball of mass 0 25 kg 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 1 5 m s 3 14 m s 2 3 m s 4 3 92 m s

B VA Q5 Two particles A and B are moving in uniform circular motion in concentric circles of radii r and r with speed v and VB respectively Their time period of rotation is the same The ratio of angular speed of A to that of B will be NEET 2019

Q6 An insect crawls up a hemispherical surface very slowly see the figure The coefficient of friction between the surface and the insect is 1 3 If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical the maximum possible value of a is given a a cota 3 b tana 3 c seca 3 d coseca 3

An object moves on a circular path such that its distance covered is given by the function S 2t The ratio of magnitudes of its accelerations at times t 1 sec and t2 2 sec is 1 2 The radius the circle is Write until two digits after the decimal point

3 The resultant of two vectors A and B is perpendicular to A and has the magnitude 24 cm If the sum of magnitude of A and B is 32 cm then their magnitudes are 1 5 cm 27 cm 2 7 cm 25 cm 3 14 cm 18 cm 4 10 cm 22 cm

A body is projected vertically upward from ground If we neglect the effect of air then which one of the following is the best representation of variation of speed v with time t a L K c b d d Lor t

33 A stone is tied to one end of a string and whirled in a horizontal circle of radius I m at 20 revolutions per minute Calculate the angular velocity and linear speed of the stone Also find the centripetal acceleration

A heavy disc with radius R is rolling down hanging on two non stretched string wound around the disc very tightly The free ends of the string are attached to a fixed horizontal support The strings are always tensed during the motion At some instant the angular velocity of the disc is oo and the angle between the strings is a Find the velocity of centre of mass of the disc at this moment 2RT 1 x cosa a

If m is mass of electron u its velocity r the radius of stationary circular orbit around a nucleus with charge Ze then from Bohr s first postulate the speed u of the electron in CGS system in the orbit is equal to Question Type Single Correct Type 1 2 mr V Ze Ze mr 70

In the circuit shown in figure cells of emf 2 1 3 and 1 V respectively having resistances 22 122 32 and 1 2 are their internal resistances respectively The potential difference between D and B in volts 1 13 10 13 3 2V 20 Hww 1V 1923 www D 202 Im ww 3 V 32 B TIV 10 2 4 2 13 7 13

1 A cyclist moving on a circular track of radius 40 m completes half a revolution in 40 s Its average velocity is a zero b 4 ms c 2 ms d 8 m s 2 The position of an object moving along xari b c d 19 Th giv

19 A wheel starting from rest is uniformly accelerated at 2 rad s for 20 seconds It is allowed to for the next 10 seconds and is finally brought to rest in next 20 seconds The total angle rotated by the whee in radian is 1 600 3 1800 2 1200 4 300 20 A body rotates about a fixed axis with an angular acceleration of 3 rad s2 The angle rotated by it during the time when its angular velocity increases from 10 rad s to 20 rad s in radian is erit Isinoshort rooma s no 1 50 e De s diw prim yo 2 100 s lo bis eno lo azem to enso ent 3 150 b9902 6 yet end to bas 4 200 pribrista a blinis ebswor oninnut enste w ovom w blirig

solid sphere and a hollow sphere each of mass m and radius Rare released from the top of an inclined plane side by side If both roll down without sliding then ratio of their translational inetic energy is at the bottom of the inclined plane is WIN

A vehicle is crossing a vertical convex bridge The force exerted by vehicle on mid point of the bridge with convex curvature moving at constant speed will O More than that of at the ends O Same as that of at the ends O Less than that of at the ends Increase in proportion of speed of vehicle

A rocket of mass 120 kg is moving vertically up at 600 m s such that gas is escaping at the rate of 1 kg per second Find out acceleration of the rocket a 2 m s c 6 m s b 5 m s d 10 m s AFMC

A block of mass m is connected with a string which is wounded over a disc of mass 2m and radius R as shown in the figure If the system is released from rest then accelerations of the block will be 2m R 0 614 2g hr min m

8 Two identical carts A and B each with mass m are connected via a spring with spring constant k Two additional springs identical to the first connect the carts to two fixed points The carts are free to oscillate under the effect of the springs in one dimensional frictionless motion Cart A k Cart B www ww O O Under suitable initial conditions the two carts will oscillate in phase according to x 1 xo sin t xB t 2 2 URE 3 2 2 where x and xp are the locations of carts A and B relative to their respective equilibrium positions Under other suitable initial conditions the two carts will oscillate exactly out of phase according to x t xo sin t XB t Determine the ratio 1 3 M 24 26 12 4 3

A small stone is tied with a string which could break at tension 400 N The stone is moving in horizontal plane with Angular speed cot Then the time at which string could break is Length of string is Im and and mass of particle is 1kg 30 sec 25 sec 20 sec None

The track shown in the figure is frictionless The block B of mass 4kg is lying at rest and block A of mass 2kg is pushed along the track with some speed The collision between A and B is perfectly elastic With what velocity should the block A start such that block B just reaches at point P P 4 m A 4 m BH

Question 11 Two point A and B are located on floor of a room as shown in figure The roon has three walls 1 2 and 3 Perpendicular Distance of point A from wall 1 2 and 3 is 0 4 m m and 3 m respectively While that of point B is 3 2 m 11m and 0 2 m respectively A man to move from point A to B touching the walls 1 2 and 3 at least once Minimum distance in meter traveled by man will be 0 4 m 3m 3 2 1 2m 2 80 2 m Im

Read the following and write the correct pairs Two light rods of length 1 m each are hinged together as shown in figure Rod AB makes an angle with vertical while rod BC makes an angle with horizontal End C of rod BC remains in contact with horizontal Rod AB is rotated with constant angular velocity 1 rad s in clockwise direction At the instant when 0 30 and 30 Match the variables in column I with values in column II Column 1 A Angular velocity of rod BC in rad s B Velocity of block D in m s C Magnitude of angular acceleration of rod BC in rad s D Acceleration of point B in m s P q r s Column II 3 3 1 3 3 3 1 6 3

13 4 1 A particle undergoes uniform circular motion The velocity and angular velocity of the particle at an instant of time is v 31 4j m s and xi 6j rad sec The value of x in rad s is A 8 50 2 B 8 The radius of circle in metres is A 1 2 m B 1 m The acceleration of particle at the given instant is A 50k B 42k 2 50 m s 3 1 T 0 1 T mv uma t g C 6 C 2m C 2i 3j 5 2 5 6 8To D can t be calculated D can t be calculated D 50k 7 5 5 8 6

A rigid object of mass m is moving in a circle of radius r with a constant speed v The force on the body is mv and is directed r towards the centre The workdone by thi force in moving the object over half th circumference of circle is 1 3 mv Tur 2 r 2 mv 2 r 4 zero

P2 R an angular velocity of 240 rev min in 10 s then its ang acceleration will be 36 If a disc starting from rest acquires 1 b 3 11 rads 1 d 1 13 rads 1 llow sphere of mass mis com 1 a 1 52 rads c 2 51 rads 1 B BCECE Mains a 110

36 A car is going round a circle of radius R with constant speed Another car is going round a circle of radius R with constant speed If both of them take same time to complete the circles the ratio of their angular speeds and linear speeds will be 1 3 R R VR R 1 R R 2 1 1 R 4 R 1

System of Particles and Rotational Motion 10 A disc of radius 2 m and mass 100 kg rolls on a horizonta floor Its centre of mass has speed of 20 cm s How much work is needed to stop it a 3 J b 30 kJ c 2 J d 1 J

3 Two particles A and B are moving in uniform circular with speed motion in concentric circles of radii r and A IB VA and VB respectively Their time period of rotation is the same The ratio of angular speed of A to that of B will be a I IB A C TB TA b VA VB d 1 1

A massive homogeneous rope of length 1 is suspended between two nails A and B driven in the same horizontal level The rope makes angle 9 with the horizontal at the nails and its lowest point is at a depth d below the nails A bead threaded in the rope released from the nail A slides down the rope without friction If the bead is so light that the shape of the rope remains unaffected find acceleration of the bead when it passes the lowest point of the rope 0 d

LANG AY Alejandro forgot to fasten his seat belt when he got onto the roller coaster Read the descriptions of his ride Then answer the question 1 As the coaster climbed uphill Alejandro felt pushed back against his seat 2 When he went down the first hill Alejandro felt pushed back against his seat again but for a different reason than when he was climbing uphill 3 The coaster went through a series of loop the loops and Alejandro was turned upside down but he did not fall out for a third reason What forces explain Alejandro s experiences at each of the three parts of his roller coaster ride Describe his experiences in sentences

A small sphere of mass m suspended by a thread is first taken aside and released when the string becomes horizontal Select the correct alternative A The acceleration of the sphere when string makes angle with vertical is g 1 3 cos 0 B Thread tension as a function of e is T 3 mg cos 0 C When the tension is mg the vertical component of velocity of sphere is maximum D The tension has a maximum value 3mg

A particle of mass m moves in a circular radius 2m with a speed of 10m s Calculate the time after which the magnitude of change in its momentum becomes equal to its initial momentum 1 T 15 sec T 3 sec 2 2 15 sec 4 Not possible