Rotation Questions and Answers

From a circular small disc of radius a as shown The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is 1 MR 3 MR R is removed from the disc 2 R 13 MR 8 4 MR

m and side a is free to rotate about a vertical axis passing through its centre O The platform is stationary and a person of the same mass m as the platform is standing on it at point A The person now starts walking along the edge from A to B see figure The speed v of the person with respect to the platform is constant Taking v 5 m s and a 1 m 2 Answer B Bi Your Attempt C Rate this question Angular velocity of platform A when the person is at A is 6 rad s Correct answer Angular velocity of platform increases first and then decreases again as it reaches B Angular velocity of platform decreases first and then increases again as it reaches B Angular velocity of platform

A solid sphere and hollow sphere of the same mass and radius are given a spin about their centre of mass and then they are placed on a rough horizontal surface The spin angular velocity is the same for both the spheres and it is equal to wo Once the pure rolling starts let v and be the linear speeds of their centres of mass then A B C D V1 V2 V1 V2 V1 V2 Data is insufficient

3 Kinetic energy A rod of weight 50 N is supported by two parallel knife edges P and Q and is in equilibrium in a horizontal position The knives are at a distance 10 cm from each other The centre of mass of the rod is at distance 3 cm from P The normal reaction on P is 1 50 N 3 35 N 2 100 N 4 20 N

A body of mass m is moving along a straight line from A to B with constant velocity v as shown Let LA Lg be the magnitude of angular momentum at point A and B with respect to origin then y m 4 A 0 1 LA LB 2 LA LB 3 L 1 m B x m

A 60 cm metal rod M is joined to another 100 cm metal rod M to form an L shaped single piece This piece is hung on a ply at the joint A The two rods are observed to be equally inclined to the vertical as shown The two rods are equally thick If the ratio of density of M to that of M is n then value of is 18m 25

A rod of mass m is kept in equilibrium as shown in 2 figure The movable support is moved towards right The normal reaction from movable support Fixed support 1 Increases continuously 2 Decreases continuously Movable support 3 First increases then decreases 4 First decreases then increases

A uniform rod of mass m and length 2 lies on smooth horizontal surface A particle of same mass m is connected to string of length I whose other end is connected to rod Initially string is taut and both rod and string lies in same horizontal plane with 90 angle between them If particle is given initially velocity v perpendicular to string then just after giving velocity v to particle A B A linear acceleration of centre of mass of rod will be v 4l B angular acceleration of rod will be 6v 5t C tension in string will be mv 51 D angular velocity of rod will be v 21

Inner and outer radii of a spool are r and R respectively A thread is wound over its inner surface and placed over a rough horizontal surface Thread is pulled by a force F as shown in fig then in case of pure rolling R A Thread unwinds spool rotates anticlockwise and friction act leftwards B Thread winds spool rotates clockwise and friction acts leftwards C Thread winds spool moves to the right and friction act rightwards D Thread winds spool moves to the right and friction does not come into existence

Which of the following statements is are correct about forces and their torques acting on an object The object may not be in translational and or rotational equilibrium A Torque of resultant of forces acting at same point is equal to resultant of torques of these forces in an inertial frame of reference B In a non inertial frame of reference the point of application of pseudo force must pass through the centre of mass C The point of application of resultant force is the center of mass of the object when multiple forces are acting on the object D If the net force on the object is zero in an inertial frame of reference net torque in any inertial frame of reference about any point in space has same magnitude and direction

Newton s second law for translational motion in the xy plane is F ma Newton s second law rotation is t Ia Consider the case of a particle moving in the xy plane under the influence single force a Both F ma and t la must be used to analyze the motion of this particle b Either EF m or t la can be used to analyze the motion of this particle c Only F m needs to be used to analyze the motion of this particle d Only T la can be used to analyze the motion of this particle

Statement 1 A pair of upright metersticks with their lower ends against a wall are allowed to fall to the floor One is bare and the other has a heavy weight attached to its upper end The stick to hit the floor first is the weighted stick Statement 2 The torque acting on weighted stick is more than the bare stick A Statement is true statement 2 is true and statement 2 is the correct explanation for statement 1 B Statement 1 is true statement 2 is true and statement 2 is not the correct explanation for statement 1 C Statement 1 is true statement 2 is false D Statement 1 is false statement 2 is true

A thin plank of mass m is kept on two rollers such that the centre of mass of the plank is midway between the points of contact with the rollers Friction is sufficient everywhere to prevent slipping A force F whose magnitude can be varied is applied parallel to the plank as shown in figure A System cannot remain in equilibrium if F is greater than mg sin B Friction on the plank on both contact points is always directed towards F if the system is in equilibrium C Direction of friction on roller at points C and D is towards right if the system is in equilibrium If the centres of the rollers are clamped to the surfaces below it so that they cannot show translational

A rod shown above is placed inside a non viscous liquid which is homogeneous in nature and stationary The rod is pivoted at its lower point Q and is free to rotate in a vertical plane about a horizontal axis passing through P Given T1 T2 The rod is then displaced by a small angle alpha from its equilibrium position and then released The angular frequency is found to be xg T2 T1 2T1L for this SHM The value of x is

d 5 Xx The total torque about pivot A provided by the forces shown in the figure for L 3 0m is AMU Med 2012 a 210Nm b 140Nm c 95 Nm d 75Nm 90 N A 160 80 N 90 30 60 N 70 N 1609 50 N B

In the shown figure if all the surfaces are smooth and the two masses are allowed to move then centre of mass of the system will move A B upwards downwards Correct Answer Your Answer

Ing of mass M and radius R is rotating with angular speed about a fixed vertical axis passing through its centre O M with two point masses each of mass 8 masses can move radially outwards along two massless rods fixed on the ring as shown in the figure At some instant the 8 angular speed of the system is and one of the masses 9 is at a distance of 335 R from O At this instant the distance JEE Advanced 2015 of the other mass from O is a 1 5 3 5 w N R at rest at O These b R c R O 7 8 A hori around instant centre angula a D b De c Re d Inc A parti shown about C a mu b mu c mu

24 A disc of radius R 2m moves as shown in the figure with a velocity of 2vo The 6vo translation of 6v of its centre of mass and an angular velocity of R distance in m of instantaneous axis of rotation from its centre of mass is A 3 B 4 C 5 D 6 R 2v R

In any operational amplifier if two input signal are given at 45 volt and 35 volt at positive terminal and negative terminal simultaneously The circuit is working with open loop gain of 10 then solve following If gain is changed from 10 to 20 then find output voltage of amplifier Calculate common mode rejection ratio of amplifier if output voltage is 100 volt If input voltage at positive terminal is changed from 45 volt to 55 volt then find output voltage of amplifier keeping gain of 10 Calculate CMRR if voltage is changed at positive terminal from 45 volt to 55 volt and ouput voltage is 100 volt Determine the output voltage of operational amplifier

In the given network below with switch S closed and steady state condition reached find the initial conditions with justification With switch S open at t 0 find the current i t in the loop without applying transform network 8 XS 4V 292 31H 292 0 25 F

Calculate the forces in the bars of the truss shown Take A as a hinged support and C as roller support The force at B is P 10 KN in horizontal direction and that at D is PKN in the vertical direction 2m 30 PKN 2m 2m P 10 KN

A uniform solid cylinder of mass 0 3 kg starts descending from rest at time t 0 under the gravitational force see figure Find the instantaneous power in watt developed by the weight of the cylinder at t 2 s g 10 m s 9

and 53 Two stars of masses m m distance r apart revolve about their centre of mass The period of revolution is a 21 c 2n 3 r V2G m m 2r3 G m m b 2 d 2n r m m 1 3 r G m m

The figure shows two cases A and B where in case A ring of radius R is rotating with angular velocity w about its axis at rest while in case B a ring is doing pure rolling on a horizontal surface with angular velocity w Find the ratio of radius of curvature of point Q as seen from point P on ring at the given moment in case A to the absolute radius of curvature of Q in case B R P A B R

8 A circular disc reaches from top to bottom of an inclined plane of length L When it slips down the plane it takes time t When it rolls down the plane it takes time t The value of 2 is value of x will be 3 The

A square plate of mass 6 kg and side 2 m hinged about its centre on a smooth horizont plane initially it is at rest A particle of mass 1 k is moving with velocity 3 2 m s as shown the figure The particle hit the comer of th square plate and stick to in The square pla starts rotation Find the final angular velocity the square plate 1 3 rad s 45 2 2 rad s

A thin 2 m long horizontal nonuniform bar can freely rotate about a pivot at its left end as shown The mass density of the bar is given by 3 4 14 x 10 kg m where x is measured from its left end 6 1 Two forces are applied to the bar as shown at fixed angles relative to the bar The force F is applied at the midpoint of the bar and has a constant magnitude of 4 N while the force F applied at the endpoint of the bar has a magnitude that varies in time as F t 6 N Take counterclockwise as the positive direction At t 0 the bar is at rest and the rotation occurring in the horizontal plane a 1 What is the exact rational number moment of inertia of the bar about the pivot Ipivot kg m b 2 What is the exact kinetic energy of the rod as a function of time K t F F2 3 5

7 Oscillating Disk 3 Points A solid disk of mass mand radius ris on a level surface the coefficient of sliding and static friction is u A horizontal spring is connected to the axle of the disk so that the disk can roll back and forth the other end is connected to a fixed point on the wall The spring constant is k and the equilibrium length of the spring is L Spring Omy a Determine the maximum amplitude Amax of the back and forth oscillations of the disk so that it does not slip while rolling b Assume that the disk starts out from rest with an amplitude of 2 Amax Determine the fraction of the initial potential energy of the system that will be dissipated through friction as heat

3 A particle is moving with a constant velocity along a line parallel to positive X axis The magnitude of its angular momentum with respect to the origin is a zero b increasing with x c decreasing with x d remaining constant E

A roller having radius 40cm and weight 3000N is to be pulled over a curb of height 20cm as shown in fig 2 by a horizontal force applied at the end of a string wound round the circumference of the roller Find the magnitude of the horizontal force which will just turn the roller over the corner of the rectangular block Also determine the magnitude and reaction at A and B Consider all the surfaces as smooth 40 cm cm 20 cm DW A Fig 2 B Block Ra CO 1

17 A solid sphere is rolling without slipping on a level surface at a constant speed of 2 0 ms How far can it roll up a 30 ramp before it stops The moment of inertia of the sphere about its axis of rotation is 2 mr 5

ed signal is plotted below 10V SV V t 100 s Which one of the following best describes the above signal 1 9 sin 2 5 105 t sin 2 10 t V 2 9 sin 4 x 104 t sin 5 10 t V 3 1 9sin 2 104 t sin 2 5 10 t V 4 9 sin 2 104 t sin 2 5 10 t V

8 63 64 The uniform sign has a weight of 1500 lb and is supported by the pipe AB which has an inner radius of 2 75 in and an outer radius of 3 00 in If the face of the sign is subjected to a uniform wind pressure of p 150 lb ft2 determine the state of stress at points C D E and F Show the results on a differential volume element located at each of these points Neglect the thickness of the sign and assume that it is supported along the outside edge of the pipe N B 6 ft 3 ft 12 ft D C 150 lb ft

16 A linear rod of mass m length is placed as shown in figure such that its one end rests on a rough table of friction coefficient u When string BS is cut rod AB starts falling from rest At an angle 0 tan rod starts slipping on the table find x S 2 2x

25 A cylinder of diameter 2R and mass M rests on two rough pegs coefficient of static friction u the distance 2kR apart A gradually increasing torque t is applied as shown The cylinder will topple before it slips if TRUE k 1 k A H gito lo ining sri B k 1 k 26 T 2kR D 1 k nt Cand a force F acts at A as shown in figure C 1 k

A uniform disc of mass m and radius R is rotating with angular velocity on a smooth horizontal surface Another identical disc is moving translationally with velocity v as shown When they touch each other they stick together The angular velocity of centre of mass of the system after contact will be A zero 2v Ro B 6R C D MNR MR W JM W l REVIEW BOOKLET 2021 JEEM PART I PHYSICS 082 R 3 ty W 21 kapr 4 5 4 14 JmR w G W MA 3 MR w 2m Y

mass M and radius R is released from rest at the top of the inclined of length I as shown which is angled at 37 from the horizontal table The table is a heighth above the floor The cylinder rolls without slipping down the incline and across the table It lands on the floor a distance D from the edge of the table a Determine the kinetic energy of the wheel as it reaches the table and as it reaches the floor b Determine the angular velocity magnitude and direction just as the wheel reaches the floor Is angular momentum conserved while the cylinder is rolling down the incline c Find the acceleration of the center of mass of the hollow cylinder as it rolls down the incline d What is the coefficient of static friction e What is the distance D M R

pjective Question II One or more correct option 1 The moment of inertia of a thin square plate ABCD of uniform thickness about an axis passing through the centre and perpendicular to the plane of the plate is 1992 2M a 1 c 1 1 b 3 14 d 1 13 14 of B 3 where 1 12 1 and I are respectively moments of inertia about axes 1 2 3 and 4 which are in the plane of the plate

A uniform disc of surface mass density o exists in space Its radius is R A small disc of radius R 2 is cut from it 15 as shown in the figure The moment of inertia 1 about axis AB is OTR Find the value of K 16K R R 2

MCQ 6 Two forces are applied on a piece of wood that is attached to a hinge as shown below The piece of wood does not move The force exerted on the wood by the hinge is a Zero b North y c South y d At an angle theta South East direction e At an angle theta South West direction f Is in some other direction hinge Big force Small force

A uniform ball of mass 6 kg and radius R rolls smoothly from rest down a ramp at an angle of 0 30 to the horizont What is the magnitude of the frictional force between the ball and the ramp as it rolls down without slipping O 8 4 N O 10 3 N O 5 7 N

m from its left end The beam s center of mass is at the center of the beam A weight W is placed at the left end of the beam to hold the it at equilibrium ds on the end of a beam weighing 1 60 kN that is balanced on a pivot placed at 1 00 18 marks 1 00 m W 2 00 m 3 00 m Mg 1 60 kN G a By choosing the pivot point as the axis of rotation find the magnitude of the weight W b Calculate the vertical force the pivot point exerts on the beam

In the arrangement shown the string does not slip over pulley Consider pulley as a solid cylinder of mass 4m and radius R The acceleration of block A is Am g 2 0 3 2m B

P3 A solid cylinder of radius 10 0 cm and mass 12 0 kg starts from rest and rolls without slipping a distance 5 0 m down a roof that is inclined at angle 30 degrees The moment of inertia of a solid cylinder about its center is MR where M total mass and R radius of the cylinder 12 marks a Calculate the moment of inertia I of the cylinder b What is the angular speed w of the cylinder about its center as it leaves the edge of the roof c What is the linear velocity at the edge of the roof d The roof s edge is at a height H of 5 0 m How far horizontally from the roof s edge does the cylinder hit the ground

MR The ball is released from rest and A solid ball of mass M and radius R has a moment of inertia of I above the point where it leaves the rolls down the ramp with no frictional loss of energy The ball is projected vertically upward off a ramp without ramp Determine the maximum height of the projectile ymax if h 10 Round your answer to nearest integer loss in energy as shown in the diagram reaching a maximum height y max

4 X 0 English Mark for review A uniform solid sphere of mass M 1 kg radius R 50 cm is projected with velocity vo 1 m s and simultaneously given a reverse spin wo as shown in figure The horizontal surface is rough What is initial angular velocity wo in rad sec for which rotation and Translation stops simultaneously in subsequent motion 0

5 A movable pulley of mass my and radius r can roll on a cord which is fixed at point A passes over a fixed pulley of mass m2 and radius r2 and carries a block of mass m3 The two pulleys may be considered as circular disks Find the acceleration of the block 8ma 4m1 Am 18ma my

From a solid hemisphere of radius R a cone of base radius R and height R is removed as shown in figure The moment of inertia of the remaining body about an axis BB in the plane of the base and passing through the centre O is is the moment of inertia about AA which is parallel to BB and is moment of inertia about an axis perpendicular to BB and passing through O then A 1 1 8 1 21 C 1 1 2 2 4 B D 1 31

The moment of inertia of solid sphere is given as 2 5 Mr What is the moment of inertia of a cricket ball of mass 0 16 kg e and radius 0 036 m If its spin is 20 rad sec What is its angular momentum and kinetic energy

4 X 0 English Mark for review A solid uniform cylinder of mass m 6 kg and radius r 0 1 m is kept in balance on a slope of inclination a 37 with the help of a Thread fastened to its jacket The cylinder does not slip on the slope The minimum required coefficient of friction to keep the cylinder in balance when The thread is held vertically is given as find The value of 4 F a m