Rotation Questions and Answers

change If same torque was provided on a hard boiled egg raw egg to spin on a table then 1 Hard boiled egg will have higher angular acceleration 2 Raw egg will have higher angular acceleration 3 Both will have same angular acceleration 4 Information is insufficient

of the following are correct a For a general rotational motion angular momentum L and angular velocity a need not be parallel b For a general rotational motion angula momentum L and angular velocity an always parallel c For general translational motion Line momentum P and velocity v are alwa parallel d For a general translation motion accelerati a and velocity v are always Parallel 1 a d 2 b d

se or decrease depending upon clock wise or anticlock wise sense of rotation 10 If ice of the poles will start melting the duration of day and night 1 Increase 2 Decrease 3 Not change 4 Depend upon th 40

53 A planet of mass m revolves in an elliptical orbit around the sun so that its maximum and minimum distance from the sun are equal to r and rp respectively The angular momentum of this planet a relative to the sun is 2GMrpra V rp ra a m GMrpla V rp ra c m The b m d m 4GMrpa r ra GMrra 2 rp ra 59 magnitudes of the gravitational force at distance ro of a uniform sphere of

A thin uniform rod AB of mass m and length L is placed on a smooth horizontal table Rod is hinged at centre of mass as shown A constant horizontal Force of magnitude F starts acting on the rod at one of the ends B Initially the force is perpendicular to the length of rod Acceleration of the point on L the rod located at distance from end A just after F starts acting is nF m Find the value of n

1 A slender prismatic bar AB is supported in a horizontal position as shown in Fig A At what distance x from the hinge A should the vertical string DE be attached to the bar in order that when it is cut there will be no immediate change in the reaction at A Ans x 21 3 K AK C w FIG A E D 7 2 B

A playground merry go round of radius 1 5 m has a mass 20 kg with the shape of solid cylinder and is rotating at 10 rev min about its center of mass A 30 kg child hops onto the merry go round and manages to sit down on the edge Determine the new angular speed of the system

A uniform rod of mass 10 kg and length 2 m is placed along x axis such that its one end is at the origin Moment of inertia of the rod about z axis is 1 3 40 kg m 12 20 kg m 12 2 4 20 3 kg m 40 kg m 3

The figure shows a system consisting of 1 a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed oo and ii an inner disc of radius 2R rotating anti clockwise with angular speed wo 2 The ring and disc are separated by frictionless ball bearings The system is in the x z plane The point P on the inner disc is at a distance R from the origin where OP makes an angle of 30 with the horizontal Then with respect to the horizontal surface 2012 3R Z w 2 R 30 2R X a the point O has a linear velocity 3Rwi b the point P has a linear velocity Roi 11 4 13 4 c the point P has a linear velocity d the point P has a linear velocity Rw 3 Rol 4 3 4 Ro

Unleashing Potential 11 A disc having radius a is rising on an inclined plane as shown in figure If the acceleration of disc 2 is gsine then find the value of b Ans 3 Sol 2 mg sine mg sin 0 f nacm ma f a a 2 aam a a on solving F mg cos 1 3 4 Fixed wedge Jable TUTE 5

d If the X then t is constant 18 Two thin circular discs of mass m and 4m having radii of a and 2a respectively are rigidly fixed by a massless rigid rod of length 24 a through their centers This assembly is laid on a firm and flat surface and set rolling without slipping on the surface so that the angular speed about the axis of the rod is w The angular momentum of the entire assembly about the point O is L see the figure Which of the following statement s is are true 2016 Adv m a 4m Co 2a 20 A sph plane In th a

7 Find the average speed of the Earth as it goes around the Sun in m s Use C 2mr for the total distance the Earth travels in one revolution around the sun where r average Earth Sun distance The average Earth Sun distance is 1 5 x10 m and the time is 1 year 8 From your answer in question 7 determine the magnitude of the average centripetal acceleration of the Earth as it revolves around the Sun

Are not equal to each other in magnitude 4 Cannot be predicted 6 A wheel has angular acceleration of 3 0 rad s and an initial angular speed of 2 00 rad s In a time of 2 s it has rotated through an angle in radian of 1 10 2 12 3 4

A light rod carries three equal masses P Q and R as shown in figure The angular acceleration of Q in vertical position of rod If it is released from horizontal position e P e 2gl 3 O gl O 0 Q l R

Two threads are rotate about a fixed horizontal axis through its centre At the free end of one string a particle of mass m is attached and the free of the other string 3 mg 2 is pulled down with a constant force F Given R 2R and moment of inertia of the pulley 3 mR 4 about the axis of rotation is LL R S T m Then

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

A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure Another identical particle moving horizontally collides inelastically and sticks to it The minimum speed of moving particle so that the rod with particles performs circular motion in a vertical plane will be length of the rod is l consider masses of both particles and rod to be same m l

Consider a circular wheel rolling no slip along a flat surface The wheel has radius 0 1 m and is rotating clockwise at 2 rad s What is the direction of the absolute velocity vector in the earth fixed reference frame for the wheel s center point O the velocity is zero so it does not have a direction O to the right along 7 O to the left along 7 Odown and to the right with both 7 and components

In a bicycle the radius of rear wheel is twice the radius of front wheel If rF and r are the radius VF and V are speeds of top most points of wheel then A Vr 2VF C VF VI B VF 2Vr D VF Vr

A rigid body is rolling without slipping on the horizontal surface A 2 3 60 A 00 Column I Velocity at point A i e VA 1 Velocity at point Bie VB 2 Velocity at point Cie VC 3 Velocity at point D i e VD 2 1 B 1 EVE B B C 4 D B T Column II VV2 Zero V 2V

A ring and a disc of different masses are rotating with the same kinetic energy If we apply a retarding torquet on the ring it stops after making n revolutions After how many revolutions will the disc stop if the retarding torque on it is also t A B n C 2 D 2n 4n

Two small blocks tied with a massless string of length 3 m are placed on a rotating table as shown The axis of rotation is 1 1 m from 1 2 kg mass and 2 m from 1 kg mass The angular speed w 1 rad s and the blocks do not slip Surface below 1 kg block is smooth and that below 1 2 kg block is rough friction coefficient 0 6 Choose the correct option s 1 2 kg 1 m Tension in the string is 2 N Tension in the string is 1 N 2 m 1 3 Friction force on kg block is N 1 kg

A uniform solid sphere of mass m and radius R is imparted an 2V0 and then placed on initial velocity vo and angular velocity R a rough inclined plane of inclination 0 and coefficient of friction 2tane as shown The time after which the sphere will start rolling without slipping is A C Vo 2gsin0 Vo 6gsine B D 4gsin0 Vo 8gsin 0 2V R m R Vo 2 tane

Just after release of rod as shown on smooth 2a horizontal track Find the ratio 2 a is acceleration of point A and a is angular acceleration of rod just after release vertical 777 60 A massless string 60 B 60 uniform rod 77 where

59 A uniform disc of radius R 2 3 m is moving on a horizontal surface without slipping At some instant its angular velocity is 1 rad s and angular acceleration is a 3 rad s TT C A 0 B P 777777 Re da a Find acceleration of the top point A b Find acceleration of contact point B c Find co oridnates r 0 for a point P which

A scaffold of mass 79 kg and length 7 6 m is supported in a horizontal position by a vertical cable at each end A window washer of mass 67 kg stands at a point 1 6 m from one end What is the tension in a the nearer relative to the person cable and b the farther relative to the person cable

A uniform equilateral wire frame in vertical plane having mass 3m and length at each side I is hinged at A Two ideal mass less springs of force constants k and k are attached as shown in the fig The frequency of small oscillations about A in vertical 1A Ck k 3g 38 2n B 4m 3m acceleration due to gravity 8 AYANA GROUP plane is given by xxxxxxxxx AB then find the value of is K xxxxx co

17 The moment of inertia of a solid sphere about an axis passing through centre of gravity is MR then its radius of gyration about a parallel axis at a distance 2R from first axis is Tord s Tur and 34 fe 1 5R id quia fa 2 4 22 R 3 5R 2 MR 4 12 R 2R

Marking scheme 4 for correct answer 0 if not attempted and 1 in all other cases 5 A hollow cylinder of radius 4R is rotating about fixed horizontal axis passing through point O with angular velocity A solid cylinder of radius R is rolling without slipping with respect to inner surface of hollow cylinder At the given instant the line OC has angular velocity of 20 Point A and B are topmost and bottom most points c solid cylinder respectively and C is its centre Then at the given instant 80

20 A particle moves along a circle of radius m with constant tangential acceleration If the velocity o T the particle is 80 m s at the end of the second revolution after motion has begin the tangential acceleration is 45 44 45447 2xi tela aru ya ya faus fava 20 m qu U qu Ia ada and di aft 340 80 m s zus trata ca 1 40 ms 2 640 ms 3 160 ms 4 40 ms

69 The triangular plate described in the last question has angle A 0 Now find its moment of inertia about an axis through A perpendicular to the plane of the plate same A 0 a a B

3 F F A thin circular ring of mass M and radius r is about its axis with a constant angular velocity w Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring The ring now rotates with an angular velocity 1 2 3 4 M m M 00 M 2m M 2m COM M 2m M 2m

3 A uniform solid sphere of mass M and radius r shown in the figure slips on a rough horizontal plane At some instant it has translational velocity vo 25 vo and rotational velocity about the centre Find the translational velocity after the sphere starts pure rolling 5 1 7 0 V 25 V S 2 6 7

18 A force F 31 41 N is acting on a point mass 1 kg at a point A 2m 2m Find the 2 angular acceleration of the line OA at this instant m 1 1 rad s 3 rad s A 2 1 1 2 4 1 rad s rad s

The density of a rod gradually changes from one end to the other It is pivoted at one of the end so that it can rotate about a vertical axis through the pivot A horizontal force F is applied on the free end in a direction perpendicular to the rod The quantities that depend on axis of rotation in this situation are angular acceleration B Total kinetic energy of the rod when the rod completes one revolution C Angular momentum when the rod completes one revolution Angular velocity of rod

A thin rod is hinged at one end O and it is in an unstable equilibrium position It falls under gravity due to a slight disturbance It makes angles 60 90 and 180 with vertical in positions 2 3 and 4 respectively If 2 03 04 are angular velocities at these positions then A 4 203 B 04 20 C 4 1 5 2 D 004 2002 O 60 90

When a body is in pure rolling on a horizontal surface A its point of contact slips with respect to the surface its point of contact moves with the speed and acceleration of the surface its centre of mass moves along a straight line D its top most point always move faster than the lowest point of contact

A uniform disc of radius 20 cm is performing 20 pure rolling on a moving surface if it s angular velocity is 5 rad s then find velocity of it s centre of mass 1 1 m s 3 3 m s V 2 m s 2 2 m s 4 None of these ER TEST SERIES JOINT PACKAGE COURSE 1 1 m s 3 3 m s 20 cm from the citea 35 rad saat 3 C V 2 m s 2 2 m s 4 0999DMD31032000

53 From a circular disc of radius R and mass 9M a small disc of R radius is removed as shown 3 in figure The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is a 4 MR c 40 MR b d 40 9 37 R 3 RO MR MR2

20 The 51 0cm diameter disk rotates counterclockwise on an axle through its center F1 62 2N F2 74 5N F3 74 5N F4 62 2N and d 7 51cm What is the net torque about the axle Let the counterclockwise direction be positive Fa d 469 d X

An extended object is initially at rest on a frictionless horizontal surface as shown in the figure At t 0 the forces F F2 and F3 start applying on the object The net force acting on this object is equal to Fnet F F2 F3 and the net torque acting on the object with respect to an axis perpendicular to the table and passing through the center of mass marked with CM is equal to 7 net 71 72 73 What can we say about the motion of this object Mark all that apply F F3 CM F Select one or more a If Fnet 0 but net 0 the center of mass of the object will stay at rest but the object will start

An object is pivoted at point P A student ties a length of string to a peg on the object He pulls the string with a force F peg B Fxr What is the moment of the force F about the point P A Fxq string C Fxs object D Fxt

4 103 A wedge of mass m and triangular cross section AB BC CA 2R is moving with a constant velocity vi towards sphere of radius R fixed on smooth horizontal table as shown in figure 4 156 The wedge makes an elastic collision with the fixed sphere and returns along the same path without any rotation Neglect all friction and suppose that the wedge remains in contact with the spare for a very short time A during which the sphere exerts a constant force F on the wedge a Find the force F and also normal force N exerted by the table on the wedge during the time At 2my b Let h denote the perpendicular distance between the centre of mass of the wedge and the line of action of F Find the magnitude of the torque due to the normal force N about the centre of the wedge during the interval At 1 A B Figure 4 156 LY 2mv 4mvh

A ladder with a mass of m kg uniform mass and a length L is leaning against the corner of the top of a wall The contact point between the corner of the wall and the ladder is at 0 750L from the bottom of the ladder The angle between the ladder and the ground is 0 A painter of mass M kg is standing on a ladder rung L 3 from the bottom of the ladder and sees a paint can of mass m1 kg hanging from the very top of the ladder What is the magnitude of the force from the wall on the ladder if this force is straight up

tional equil only 8 A 1200 kg car moves in horizontal circular track of radius 20 m The separation between the two back tyres is 1 7 m The center of mass of car is 0 5 m Find the coefficient of friction between road and tyre so that car slips before toppling A 1 7 B 1 7 C 3 4 D 3 4

Three bodies a ring a solid cylinder and a solid 21 sphere roll down the same inclined plane without slipping They start from rest The radii of the bodies are identical Which of the bodies reaches the ground with maximum velocity 1 Ring 2 Solid cylinder 3 Solid sphere A B C S gam a f f 1 R 2 3

A hollow sphere is performing pure rolling then 9 find acceleration of it s centre of mass F M 1 3 6F 5M 2F 3M R Rough 2 3F 5M Telegram ne questionga 4 None of these 1 1 a 6F SM 2F 3M Mtaala a M R Rough 2 F 3F SM 4 F

Two objects are connected to a rope and the rope is hung over a pulley connected to the ceiling as shown in the figure below M1 MOR My The masses of the objects are m 16 0 kg and m 11 0 kg the mass of the pulley is M 5 00 kg and the radius of the pulley is R 0 300 m Object m is initially on the floor and object m is initially 4 80 m above the floor when it is released from rest The pulley s axis has negligible friction The mass of the rope is small enough to be ignored and the rope does not slip on the pulley nor does it stretch a How much time in s does it take object m to hit the floor after being released At b How would your answer to part a change if the mass of the pulley were neglected Enter the time in seconds it takes object m to hit the floor if the mass of the pulley were neglected

7 A painter ladder is formed by joining two uniform ladders each 3m long and weighing 150 N Both the ladders are hinged at the apex and are held together by a horizontal tie rope on a smooth floor If a 50 kg load is suspended from the apex as shown in figure then determine the tension in the tie rope 3m 1 6 www Tie Rope 0 5m k4m

From a uniform circular disc of radius R and mass 9M a small R disc of radius is removed as shown in the figure The 3 moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is 37 M 1 9 40 MR2 2 4 MR 4 10 MR R