Rotation Questions and Answers

Consider the sphere moving on horizontal surface At some instant it has linear velocity vo and angular velocity about center Vo of mass 2R The translational velocity after the sphere starts pure rolling Vo 2R 1 2 3 4 5vo 7 6V0 7 3V0 4 3V0 Vo

Respected pls give detailed solution with diagram of the following questio n 2 A ring of diameter 2 m oscillates as a compound pendulum about a horizontal axis passing through a point at its rim It oscillates such that its centre moves in a plane which is perpendicular to the plane of the ring Find the equivalent length of the simple pendulum

12 A semicircular disc of mass M and radius R is free to rotate about its diameter The moment of inertia of semicircular disc about a line perpendicular to its plane through centre is 3 MR 4 MR 3 a C b d MR 2 MR 4

5 A uniform cylinder has a radius R and length L If the moment of inertia of this cylinder about an axis passing through its center and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its center and perpendicular to its length then AIIMS 2010 1 L R 3 L R 5 2 L 3R 3 4 L R

Four particles each of mass m are placed at the corners of a square of side length l The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is Question Type Single Correct Type 1 2 l 2 NI 2

The diagram shows a uniform disc of mass M radius a If the moment of inertia of the disc about the axis XY is I its moment of inertia about an axis through O and perpendicular to the plane of the disc is 1 Ma Question Type Single Correct Type 2 I Ma 4 a 2 al cm

1 Three point masses each of mass m are placed at corners of an equilateral triangle of side L The moment of inertia of this system about an axis along one side of the triangle is 1 mL 3 3mL 2 4 3mL 4 3mL

36 A galvanometer together with an unknown resistance in series is connected across two identical batteries each of 1 5 V When the batteries are connected in series the galvanometer records a current of 1A and when the batteries are in parallel the current is 0 6 A What is the internal resistance of the battery a r Q 313 c r Q b r 20 5 3

Point masses m and m are placed at the opposite ends of a rigid rod of length L and negligible mass The rod is to be set rotating about an axis perpendicular to it The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity wo is minimum is given by m1 X P L x m 2

A uniform disc of radius 4R has a circular cavity of radius R as shown The surface mass density of the disc is o The disc is held vertically on a rough horizontal surface such that the line joining the geometrical centre O of the disc and centre of the cavity C is horizontal If the angular acceleration of the disc just when it is released assuming that it starts pure rolling motion and does Ng then find N 717R not topple is IT

30 A wheel of radius R with an axle of radius R 2 is shown in the figure and is free to rotate about a frictionless axis through its centre and perpendicular to the page Three forces F F 2F are exerted tangentially to the respective rims as shown in the figure 2F R 2 45 R F The magnitude of the net torque acting on the system is nearly a 3 5FR b 3 2 FR

97 A solid sphere rolls without slipping first horizontal and then up to a point X at height h on an inclined plane before rolling down as shown The initial horizontal speed of the sphere is 10gh 7gh V 5 a c V 7 5gh 7 X b d 2gh

A disc of radius R is rolling without slipping on a floor as shown in the figure If velocity of its centre of mass is vo then velocity of point P at the instant R shown is OP 2 1 Vo Pa 300 2 Up 2V Cos 2 2V cose VO 7 2

17 Four identical rods are joined end to end to form a square The mass of each rod is M The moment of inertia of the square about the median line is a c M1 3 M1 6 b M12 4 d none of these of inertia of the system about an

uniform disc of radius R and mass M a 12 From square plate is removed as shown in figure The moment of inertia of remaining body about an axis passing through the centre O of the original disc and perpendicular to its plane is MR 1 1 2 3 MR 1 3 R O MR 1 1 2 4 MR 2 1 2

9 An object is made by removing a D shaped chunk from a cylinder of radius R m is the mass of the object and the object is kept on a rough incline see in figure The friction between the object and the incline is sufficient to prevent sliding At a given instant the object has an angular velocity At the given instant the angular acceleration of the object will be A Independent of R B dependent on m C Dependent on w D dependent on coefficient of friction between the object and incline T Id ing 13 he Da

A ceiling fan of moment of inertia 30 kgm rotates about its own axis at a speed of 120 r p m under the action of an electric power 62 8 watt If electric power is cut off how many rotations will it complete before coming to rest

CONS 99 A solid circular shaft of diameter d and length L is subjected to a uniformly distributed load of intensity w throghout its length while its two ends are simply supported on the two bearings The maximum deflection of the shaft is given by 4 3w L 2nd 5w L 3nd 5w L4 w L 6ad nd a b c d

How long does it take for a disc to roll down an inclined plane of length 10m without slipping The inclination of the plane is 30 Take g 9 8ms Write the answer in s Round the answer to two decimal places

60 ABC is a right angled triangular plate of uniform thickness The sides are such that AB BC as shown in figure I I2 and 13 are moments of inertia about AB BC and AC respectively Then which of the following relation is correct a 4 1 13 c 13 1 1 10 I B b I 13 d I3 4 1 3 12 66

243 Two solid rods labeled A and B have the same mass but lengths 3L and 4L If they rotate about their centers with the same angular frequen of the angular kinetic energy of rod A compared to rod B A 3 4 8 4 3 O c 9 16 Om 16 9 Chat

A train 1 moves from east to west clockwise and another train 2 moves from west to east anticlockwise on the equator with equal speeds relative to ground The ratio of their centripetal acceleration relative to centre of earth is 1 1 3 1 a a2 2 1 4 1

A force F Mg is applied on the top of a circular ring of mass M and radius R kept on a rough horizontal surface If the ring rolls without slipping then minimum coefficient of friction required is O F

0 9 6 ring of radius 2r the mass remaining the same If a disc of mass m and radius r is reshaped into a radius of gyration about centroidal axis perpendicular the to plane goes up by a factor of a 2 b 2 c 2 2 main constant ntum of the sphere horizonta d 4

A horizontal force F is applied at the top of an equilateral triangular block having mass m The minimum coefficient of friction required to topple the block before translation will be ma faydlar zile vildi uz str fa fal alal i Zaky ya A 4 4 4 B 117 B F a WWW 0 D None of these

15 A uniform wire frame of linear mass density having three sides each of length 2a is kept on a smooth horizontal surface An impulse J is applied at one end as shown in the figure P is the midpoint of AB Now answer the following question X A P The angular velocity of system just after the impulse 3J 3 J A B 222a 1149 112 a B D 2J 11 a

An unmanned space probe of mass m and speed v 2 km s relative to the Sun approaches the planet Jupiter of mass M m and speed V relative to the Sun as shown in the figure The spacecraft rounds the planet and departs in the opposite direction The mass of Jupiter is very much greater than the mass of the spacecraft M m and it orbits the sun at a distance of 59 AU where I AU is the orbital radius of the earth around the sun 1 AU 1 5x 10 km 1 carth year 107 s nearly The speed of the space probe after it leaves the solar system relative the sun is nearly 20 n km s where n is an integer Find the value of n M

The uniform cubical slab of side a is released from rest in the position shown in the figure For what value of x is the angular acceleration maximum friction between the surface and cube is sufficient to prevent any slipping a a

QA solid sphere of mass M and radius R rolls without slipping on a rough horizontal surface with centre of mass velocity v What is the angular momentum of the sphere about the point of contact A MV R B C 2MVR 7 7MV R 5

A smooth uniform rod of length L and mass M has two identical beads of negligible size each of mass m which can slide freely along the rod Initially the two beads are at the centre of the rod and the system is rotating with angular velocity about an axis perpendicular to rod and passing through the mid point of rod There are no external forces When the beads reach the ends of the rod the angular velocity of the system is 1 M M 3m M 6m 00 0 000 2 7 M L 1 2 M 6m a 0 00 9

Example 5 Two 100 g blocks hang at the ends of a light flexible cord passing over a small frictionless pulley A 40 block rests on the block on right and removed after 2 sec a How far will each block move in the first second after the 40 g block is removed What was the tension in the cord before the 40 g block was removed

25 A small disc of mass m placed on a plane of inclination 0 cos 0 8 with the horizontal is connected from a nail driven into the plane with the help of a light inextensible cord of length 1 1 0 m Coefficient of friction between the plane and the disc is u 3 8 The disc is held on the plane stretching the cord horizontal as shown in the figure and released Find maximum speed of the disc and angular displacement where tensile force in the cord becomes maximum during subsequent motion

A body is rolling down an inclined plane without slipping If kinetic energy of rotation is 40 of kinetic energy of translation then the body is O ring O cylinder O hollow ball O solid ball M

We have got two vertical track of equal radius One is smooth and other is rough One small solid sphere is to be projected from the bottom of the circular tracks It is seen that when it is projected on the smooth track the minimum linear speed is u to reach the top of the track and in case rough track it is u angular velocity u r where r is the radius of the sphere Assuming no slipping between the sphere and the rough track the ratio of u to u is 1 05 27 05 17

The axis of rotation of a purely rotating body 1 Must pass through the centre of mass 2 May pass through the centre of mass 3 Must pass through a particle of the body 4 None of these

C 28 The shortest distance of a planet from the sun is r and in this position its speed is v What is the speed of the planet when it is farthest from the sun Take the maximum distance of the planet S

A string wrapped on a pulley of moment of inertia T Other end of the string is connected to block of mass m as shown If m is released from rest then kinetic energy of block when it descends by h is m 1 mgh 3 Less than mgh 2 Greater than mgh mgh 2 4

7 A rod AB of mass M and length L is lying on smooth horizontal surface A particle of mass m travelling along the surface hits the end A of the rod with velocity Vo in direction perpendicular AB If the collision is elastic and particle comes to rest after collision then A M 1 Maxim C Maximum tension in the rod is m 9MV 201 B B M L A m M 4 D Maximum tension in the rod is 9mV2 16L

QA uniform disc rotating at a constant speed in a vertical plane about a fixed horizontal axis passing through the centre of the disc A piece of disc from its rim detaches itself from the dist at the instant when it is on the same horizontal with the centre of the disc and moving upwards Then about the fixed axis the angular speed of the

Pin A weighing 300 g slides along the fixed horizontal guide as the arm OB rotates about O If 0 0 3 rad s and 0 0 5 rad s2 when 0 400 determine the forces exerted on the pin by the horizontal guide and arm OB at this instant Neglect friction 1 5 m

A cord is wound around the circumference of wheel of radius r The axis of the wheel is horizontal and the moment of inertia about it is I A weight mg is attached to the cord at the end The weight falls from rest After falling through a distance h the angular velocity of the wheel will be 1 2 3 2 gh mar 2 mgh m 2 mgh 1 2 mr 2 gh

9 Two solid spheres of different mass radii and density roll down a rough inclined plane under identical situation Their time to come down is independent of their 1 3 4 rrect Answer 4 ur Answer 1 otus incorrect Mass Radius Density All of these Add to Bookmark List A Poor Stat x Unattemptot 255 Correct 511 incorrect 23 4 Ono malo of an ideal monoatomic gas at temperature TO expands slowly accord

9 12 A heavy ball is thrown on a rough horizontal surface in such a way that it slides with a speed vo initially without rolling It will roll without sliding when its speed falls to 1 vo 2 Vo 3 Vo

A disc of mass 20 kg 3m radius rotates about its axis with angular speed 100 rad sec What is angular momentum of disc about its axis Question Type Single Correct Type 1 4500 J s 2 9000 J s 3 5000 J s

metal sphere of radius r and specific heat s is rotated about an axis passing through i entre with speed n rotations per second It is suddenly stopped and 50 of its energy is use increasing the temperature of the sphere The rise in temperature of the sphere is C 8 5m n r 14s B 2 n 2 2 n r 5s D n 10r s

circular coil and a disc having same mass roll without slipping on the horizontal with sam near velocity If the total K E of the coil is 12 J then total K E of the disc is A 6 J B 15 J C 9 J D 12 J

ring a disc and a solid sphere have same mass and radius All of them are rolled down on an mclined plane from same height simultaneously The body that will reach at the bottom last mongst is A ring B disc C ring and disc D solid sphere

Disc of mass m is free to rotate about a vertical axis A man of mass m stands near circumference Radius of disc is R Initially both are at rest Now man moves with constant spe v relative to disc along circumference Choose correct opstion s Question Type Multiple Correct Type 1 2v Angular velocity of disc is 3R 3v Angular velocity of disc is 2R 3 Velocity of man is v V

wheel of moment of inertia 2 kg m is rotating at a speed of 25 rad s Due to friction on t s it comes to rest in 10 minutes Total work done by friction is B 625 J C 50 T 25 J 16001

A thin ring having mass 100 g and radius 10 cm is rotating about its axis with frequency 1 Hz Four objects each of mass 12 5 g are kept gently to the opposite ends of two perpendicular iameters of the ring The new frequency of rotation of the ring will be A Hz 3 B Hz 3 3 H Hz 3 D Hz 4