Rotation Questions and Answers

For the tank shown in figure if time of emptying the tank from height of 16m to 4m is t then choose the correct option s y y kx O If k 1 a 4 t 12000 sec 0 If k 1 a 2 t 500 sec If k 4 a 2 t 125 sec O If k 4 a 4 t 6000 sec X hole Radius r 5 cm

Four bodies of masses 5 kg 2kg 3 kg 4 kg are respectively placed at position 0 0 0 2 0 0 0 3 0 and 2 2 0 calculate the mo ment of inertia of the system of bodies abo ut X axis Y axis and Z axis respectively

ben to emerge ondbubr Figure shows three equipotential surfaces in the ions Inloq A to ent surrounding of a point charge q If t and to be the distance between them then 1 t t q 60 V 40 V 20 V ST Ole S 2 t 1

wo sources A and B are sounding notes of frequency 660 Hz A listener moves from A to B with a constant elocity u If the speed of sound is 330 m s what must be the value of u so that he hears 8 beats per second 2 8 m s 2 2 m s 4 3 5 m s 3 0 m s

32 A boy of mass m is standing on a block of mass M kept on a rough surface When the boy walks from left to right on the block the centre of mass boy block of system a remains stationary b shifts towards left c shift towards right d shifts towards right if M m and towards left if M m celeration a Equal to g b Which dep speeds of c Which der masses of d Which de and mass 39 A particle of m and anoth proiected

B A circular ring having mass M 4 m and radius R is attached to a small smooth ring of mass m kept at point A The ring is threaded onto a horizontal fixed frictionless wire Initially the bigger ring is held horizontally alongside the wire in such a manner that initially the planes C both the rings are at 90 to each other and the planes of smaller and bigger rings are perpendicular to th plane of the paper x y plane Now the bigger ring is released from rest After release the planes smaller and bigger ranges remain perpendicular to the plane of paper x y plane 36 The speed of small ring at this instant is 5 A gR C gR 20 15 B 8 4 2 gR 85 gR y

Problem 7 20 A uniform sheet of steel is cut into the shape as shown Compute the X and Y co ordinates of the centre of mass of the piece Width of each plate is 10 cm 40 40 Sol X Y 22 5 17 5 10

12 A 1 6 kg hollow cylinder I 5mr with a radius of 0 25 m is dropped onto the center of a turntable with a rotational inertia of 0 4 kgm The turntable rotates at 45 rad s after the collision What was angular speed of the turntable before the collision

Find point of application of net force from end B such that rod have same translational and rotational effect 40N A 1 zero 3 4 cm 10cm 4cm 6cm 37 100N 2 2 cm 4 6 cm B

2 A mosquito is sitting on an L P record disc rotating on a turn table at 33 revolutions per minute The distance of the mosquito from the centre of the turn table is 10 cm Show that the friction coefficient between the record and the mosquito is greater than 7 81 Take 2 g 10 m s

2 The moment of inertia of a uniform circular disc about a tangent in its own plane is 5 4MR where M is the mass and R is the radius of the disc Find its moment of inert about an axis through its centre and perpendicular to its plane sol given date It Id MR MR 2 Id 2 MB h R

10 A sphere and a disc of same radii and mass are rolling on an inclined plane without slipping a a are acceleration and g is acceleration due to gravity Then which statement is correct 1 a a g as 3 a g ad 2 g a ad ag 4 a a g ad S

A wheel is rolling along the ground with a speed of 2 m s The magnitude of the linear velocity of the points at the extermities of the horizontal diameter of the wheel is equal to 2 2 3 m s 1 2 10 m s 3 2 2 m s 4 2 m s

Find out the angular velocity of the pulley of mass 6 kg and radius 1 m at the instant the block B stirkes the ground MA 2kg MB 5kg H 2m H 6m A H 2 m 1 B H 6 m 2 7 rad s 9 1 9 rad s 3 6 rad s 4 3 rad s If two rigid bodies with ratio of the masses 3 1 have same rotational kinetic energies if the ratio of their radius of gyration is 1 3 then the ratio of their angular velocities will be 1 1 27 2 1 3 3 9 1 4 3 1 Two rigid bodies rotating with sam velocities are brought to rest by the same torque then the correct sta 1 The rigid body with higher m inertia will take less time to cc 10 2 The angular displacement o body with lower moment of be higher 3 More work needs to be don stop the rigid body of highe inertia 4 None of the A fly wheel with moment o m is rotating about its ax velocity of 4 rad s then find of revolutions taken by t coming to rest if a retardi Nm is acting on it 1 32 2 8 3

A solid spherical ball of radius R collides with a rough horizontal surface as shown in figure At the time of collision its velocity is vo at an angle 9 to the horizontal and angular velocity oo as shown After collision the angular velocity of ball may A decrease C remains constant B increase D none of these 777

Four equal and parallel forces are acting on a rod as shown in figure at distances of 20 cm 40 cm 60 cm and 80 cm respectively from one end of the rod Under the influence of these forces the rod F F 0 A is at rest C experiences a linear motion 20 40 60 80 Ver por 30 B experiences a torque prie ni squads alugnt clup A BOBO BA TARGET PHY ENG MODULE 02104 ROTATIONA mollulie D experiences a torque and also a linear motion Z NODE02 BOBO BAV

Illustration 3 4 Two beads each of mass m are welded at the ends of two light rigid rods each of length 7 if the pivots are smooth find the ratio of translational and rotational kinetic energy of sys m Fig 3 9 m

A system of two identical rods L shaped of mass m and length I are resting on a peg P as shown in the figure If the system is displaced in its plane by a small angle 0 find the period of oscillations A 2 21 3g B 2T 2 21 3g C 2 21 3g 32 D 3 1 3g

The pulley shown has radius 20 cm MOI 0 2 kg N Spring used has force constant 50 N m The system is released from fest Find the velocity of 1 kg block when it has descended 10 cm 1 m s 2 2 3 m s m s 3 4 None of these K 50 ww Y 20 1 kg 2500 10

An annular ring with inner and outer radii R and R is rolling without slipping with a uniform angular speed The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring F F is 2005 R R R 2 4 R

Example 2 Radius of gyration of a body about an axis at a distance of 8 cm from its centre of mass is 10 cm Find its radius of gyration about the parallel axis passing through tis centre of mass

3 A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end What should be the initial acceleration in rad sec of the stick if the string is cut 3 1 g 2 3 3 g 2 g 4 4 g

A rod of mass M is hinged at A on a smooth horizontal surface and can rotate about A without friction A particle of mass m moving on the horizontal plane strikes to rod and comes at rest just after collision A Impulsive hinge reaction at A may be in forward direction during collision O B Impulsive hinge reaction at A may be in backward direction during collision C Hinge reaction can not be zero during collision D Angular momentum about A will remain conserved X

3 4 12 45 anti clockwise 9 A wheel of perimeter 4 m is rolling on a horizontal surface The displacement of the point of contact of wheel and ground when the wheel completes one quarter of revolution is 1 2 4 along tan 12 1 2 2 4 along tan 3 2 4 along tan 1 EN EN 4 2 4 along tan 1 2 T 2 with x axis with x axis 2 2 2 with x axis with x axis

38 A disc of mass M and radius R starts falling down as shown in the figure The string unwinds without slipping on the disc The instantaneous power developed by the tension is 1 Tx Ro 3 R Vam T 2 TXRw 8

A solid sphere of mass M radius R and having moment of inertia about an axis passing through the centre of mass as I is recast into a disc of thickness t whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains I Then radius of the disc will be 2006 2R A C 15 4R 15 B R D 4 2 15

A round uniform body of radius R mass M and moment of inertia I rolls down without slipping an inclined plane making an angle 0 with the horizontal Then its acceleration is 2007 gsine gsine 1 2 1 MR 2 3 1 gsine 4 1 MR gsine MR

A uniform wooden stick of mass 1 6 kg and length rests in an inclined manner on a smooth vertical wall of height h such that a small portion of the stick extends beyond the wall The reaction force of the wall on the stick is perpendicular to the stick The stick makes an angle of 30 with the wall and the bottom of the stick is on a rough floor The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick The ratio h l and the frictional force f at the bottom of the stick are g 10 ms h 3 l 16 A C h 3 3 16 16 3 3 f N 8 3 3 N B D h l 3 16 h 3 3 l 16 f f 16 3 3 N 16 3 3 N 2016

7 1999 A smooth sphere A is moving on a frictionless horizontal plane with angular speed and centre of mass velocity v It collides elastically and head on with an identical sphere B at rest Neglect friction everywhere After the collision their angular speeds are A and B respectively Then A A B C WA Let I be the moment of inortin of B WA B D B 1999

A ball of mass 160 g is thrown up at an angle of 60 to the horizontal at a speed of 10 m s The angular momentum of the ball at highest point of trajectory with respect to the point from which the ball is thrown is nearly g 10 m s 2014 1 1 73 kg m s 3 3 46 kg m s 2 3 0 kg m s 4 6 0 kg m s

Two boys A and B of masses 60 kg and 40 kg are standing on a smooth ground at points P and Q of co ordinates 10 0 0 and 10 0 0 m If they move towards each other by pulling a common string then they will meet at 1 10 0 0 m 3 2 0 0 m 2 0 0 0 m 4 2 0 0 m

28 Two wheels are connected by a belt The radius of the larger wheel is three times that of the smaller one What is the ratio of the moment of inertia of larger wheel to the smaller wheel when both wheels have same angular momentum a 3 b 6 c 9 d 12

6 A person with outstretched arms is spinning on a rotating stool He suddenly brings his arms down to his sides Which of the following is true about his kinetic energy K and angular momentum L a Both K and L increase b Both K and L remain unchanged c K remains constant L increases d K increases but L remains constant

of Particles and Rotational Motion On a rough horizontal surface a cubical block of side a and mass m is projected horizontally The torque on the block about its centre of mass till the block stops is equal to 1 Zero 2 umga 2

A particle is moving along a straight line parallel to x axis with constant velocity Its angular momentum about the origin a decreases with time c remains constant b increases with time 101 d is zero

6 Consider a body shown in figure consisting two identical balls each of mass M connected by a light rigid rod If an impulse J Mv is imparted to the body at one of its ends what would be its angular velocity L a V L M b 2v L c V 3L M J Mv d V 4L

direction by a cue at a height n t we use 1 m vo LIw 2 centre acquired a linear velocity vo The angular velo o acquired by the ball is a b Svor A 2von Sh c 2voh d Svoh

4 3 6 2 A uniform triangular plate of mass M whose vertices are ABC has lengths 2 2 figure Find the moment of inertia of this plate about an axis passing through point B and perpendicular to the plane of the plate V F M1 amf IAR 37 34 B 300 12 M C 4x6 CODING and as shown in

The moment of inertia of a hollow cubical box of mass M and side a about an axis passing through the centres of two opposite faces is equal to B A 5Ma2 3 5Ma 6 0 C 5Ma 12 buons D 5Ma2 18

Illustration 59 A horizontal force F acts on a sphere of mass M at its centre as shown Coefficient of friction between the ground and the sphere is What is maximum value of F for which there is no slipping O F f ma is ation F

a mo a b mwa A particle of mass m rotates in a circle of radius a with a uniform angular speed o It is viewed from a frame c m 2 rotating with a uniform angular speed w The centrifugal force on the particle is ve waw 2 a mo a b mwa b c 2 d wo c m 2 3 b a d mowa Alebri po fel

A rod and a block are of same mass Initially rod is in horizontal position What will be acceleration of tip of the rod just after the system is released from this position shown in figure A zero 3g m B D 3g 4 3g 3

The end A of a uniform rod AB of length l touches a horizontal smooth fixed surface Initially the rod makes an angle of 30 with the vertical Find the magnitude of displacement of the end B just before it touches the ground after the rod is released 1 3 13l 6 13 l 2 4 13 2 e

by 10m Answer 500J 3 A small cylinder starts from rest from top of large cylinder At what angle with the vertical does it lose contact with the cylinder Answer cos 4 7 9 Peak value of magnetic field if popul

upon by upward parallel forces of 2 N and 4 N at ends A and B respectively The total length of the rod AB 3 m To keep the rod in equilibrium a force of 6 N should act in the following A weigh manner Pre Medical Physics 135 0 A downward at any point between A and B C downward at a point C such that AC 1 m shows a uniform disc with mass M 2 4 kg and radius 20 cm mounted on a fixed horizontal axle Figure 12 kg hangs from a ma A LI B downward at the midpoint of AB D downward at a point D such that BD

4 A rod of length L is hinged from one end It is brought to a horizontal position and released The angular velocity of the rod when it is in vertical position is a 2g L b 3g L C g 21 d g 1 1

A wheel of radius R is placed on ground and its contact point is P If wheel starts rolling without slipping and completes half a revolution find the displacement of point P R I pole

19 A metallic ring of mass 1 kg has moment of inertia 1 kg m when rotating about one of its diameters It is molten and remoulded into a thin uniform disc of the same radius How much will its moment of inertia be when rotated about its own axis

Two identical wheels each of radius R are harnessed by connecting their azles with a rigid rod and pivotally connecting midpoints of two parallel spokes with a bar A box is placed on the bar and the assembly is made to move on a horizontal track with a gradually increasing speed maintaining rolling without slipping Coefficient of friction between the her and the box is u and acceleration due to gravity is g Find speed of the centre of the wheels at which the box begins sliding with respect to

7 A ring of mass 2n kg and of radius 0 25 m is making 300 rpm about an axis through its to its plane The tension in newton developed in ring is approximately perpendicular a 50 c 175 b 100 d 250