Rotation Questions and Answers

The position of a particle is given by r 1 2j k and momentum p 31 41 2k The angular momentum is perpendicular to Question Type Single Correct Type 1 x axis 2 y axis 3 z axis

A uniform rod AB bent in the shape of an arc of circle radius 2m is free to rotate in a vertical plane about a fixed horizontal axis passing through the midpoint of the rod The situation is shown in the figure Find the angular acceleration of the rod immediately after it is released from rest from the position shown g 10ms 2 0 07

2 A circular disc of radius of gyration 20 cm at rest is dropped over another disc of same mass but double the radius of gyration rotating with 5 rad s If both the discs club together and rotate as one body about the same axis then the new combined angular speed of the discs is 1 1 rad s 3 3 rad s 2 2 rad s 4 4 rad s

A hollow sphere of mass m rolls without slipping down an inclined plane making an angle 8 with horizontal The frictional force between the hollow sphere and the inclined is mg sine 3 2mg sin e 3 2mg sin e 5 mg sine

The diagram shows a hemispherical shell of mass m and radius R is hinged at point O placed on a horizontal surface A ball of mass m strikes the shell at point A as shown in the figure moving with velocity u 1 inclined at an angle tan and then it stops For the given shell to reach horizontal surface OP what minimum speed u is required A B u M gR 3 2gR 3 gR 5 D Not possible N

View In English A hollow hemi sphere of mass m and radius r is released from rest in the position shown Knowing that the hemi sphere rolls without sliding Determine the reaction at the horizontal surface at the instant when it has rolled through 90 1 2 3 Correct Answer 1 Status unattempted 7mg 4 5mg 2 8mg 3 5mg 3 lu

EXAMPLE 31 A metre scale AB is held vertically with its one end A on the floor and then allowed to fall Find the speed of the other end B when it strikes the floor assume that the end on the floor does not slip

EXAMPLE 23 Calculate the moment of inertia of a system of masses about the axis AB passing through the mid point of the base of triangle OR The masses m m2 and m3 are located at the vertices of an equilateral triangle of length d What will be the moment of inertia of the system about an axis along the altitude of triangle passing through m

1 A football of radius R is kept on a hole of radius r r R made on a plank kept horizontally One end of the plank is now lifted so that it gets tilted making an angle 8 from the horizontal as shown in the figure below The maximum value of 0 so that the football does not start rolling down the plank satisfies figure is schematic and not drawn to scale Plank R A sine LIR B tane K 2r C sine 2R D cose 2R

A cardboard strip is folded in shape such that the parallel sections are U rectangles of length 37 and breadth 2 and the third section is square face of side 2 It is then placed on a very rough incline plane of variable 0 with 0 slowly increased from 0 The parallel sections are along line of greatest slope At what angle will it topple for the first time

An L shaped rod OAB is being rotated by a constant angular velocity o in a vertical plane about O There is a ring of mass m that can slide along the rod frictionlessly End B of the rod has a stopper to restrain the ring from falling What angle will AB make with horizontal when the ring starts to slip towards A from B la cosa A tan g la cosa C sin B tan 1 1 D sin la g la a

7 A string is wrapped around a cylinder of mass m and radius R The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string Find a the tension in the string b the work done on the cylinder when it acquires angular velocity w c the length of the string unwound in the time the angular speed reaches w

A bar AB hinged to the foundation at A and supported by a strut CD is subjected to a horizontal force of 50 kN at B as shown in the figure Find the axial force in the strut and magnitude and direction of resultant reaction at A Im im A 90 1 5m 50 KN 1 5m m

A cylinder of mass m is kept on a inclined plane having angle of inclination 30 Axis of cylinder makes an angle 30 with line along greatest slope Assuming that cylinder rolls without slipping Acceleration of cylinder is g 6 Acceleration of cylinder is g 4 B Friction force acting on cylinder is Friction force acting on cylinder is 7mg 3 7mg 6

From a disc of radius R a concentric circular portion of radius r is cut out so as to leave an annular disc of mass M The moment of inertia of this annular disc about the axis perpendicular to its plane and passing through its centre of gravity is A M R B B M R M R C M R r D M R r

A disc is rotating about an axis through its centre of mass normal to its plane with uniform angular velocity o If another identical disc is coupled parallel to the previous disc gently then new angular velocity of the system will be 2 SIN

A uniform circular ring of radius R mass m has uniformly distributed charge q The ring is constrained to rotate about its own axis which is vertical without friction In the space a uniform magnetic field B directed vertically down ward exists in a cylindrical region The cylindrical region is co axial with B and has a radius greater than R If B increases at a dB dt a angular acceleration of the constant rate ring will 1 Directly proportional to R 2 Directly proportional to q 3 Directly proportional to m 4 Independent of Rand m

A horizontal disc of mass 1 0 kg mounted on a fixed vertical axle through its centre can rotate without friction On the disc a semicircular groove OP is cut A small ball B of mass 1 5 kg when pushed on the disc towards the centre O the ball enters the groove with a speed 2 0 m s and moves through the groove without friction With what speed will the ball leave the disc Neglect loss of mass due to cutting the groove a 1 0 m s c 3 0 m s b 1 5 m s d Insufficient information

The object shown in the figure below consists of a thin rod of length 22 8 cm and mass m 1 20 kg with a solid ball of diameter d 10 0 cm and mass M 2 00 kg attached to its top The object is free to pivot about a frictionless axle through the bottom of the rod The object is initially vertical and at rest when it starts to rotate clockwise e m M i a After the combination rotates through 90 degrees what is its rotational kinetic energy in J 6 94 X How can you apply conservation of energy to the system of the object and Earth What types of energy are changing What are the positions of the centers of mass of the rod and the ball What is the change in height of each J b What is the angular speed in rad s of the rod and ball 8 75 rad s c What is the linear speed in m s of the center of mass of the ball 17 5 X How is angular speed related to linear speed What is the distance from the pivot to the center of mass of the ball m s d How does it compare with the speed had the ball fallen freely through the same distance of 27 8 cm Express your answer as a percentage

Moment of inertia of a disc about an axis which is tangent and parallel to its plane is I Then th moment of inertia of disc about a tangent but perpendicular to its plane will be A 31 B 51 6 C 31 61 D

Two spheres of equal masses one of which is a thin spherical shell and the other a solid E the same moment of inertia about their respective diameters The ratio of their radii will be A 5 7 B 3 5 C 3 5 D 3 7

The moments of inertia of two freely rotating bodies A and B are IA and Ig respectively A IB and their angular momenta are equal If K and Ka are their kinetic energies then A KA KB B KA KB C KA KB D KA 2KB

Find the moment of inertia of a section of circular disc of radius R about an axis perpendicular to its plane as shown in the figure The section has mass m and subtends an angle 0 at the centre R PEAR R 1 2 mR2 2 2 R 30 m I AR mR2 4 4 3 3mR 4 mR

2 A disc placed on a frictionless horizontal plank is rotating with a constant angular velocity about its central vertical axis Now the plank is made to move with a constant acceleration a on a straight path If you assume initial location of the centre of disc as origin direction of motion of the plank in negative y axis of the coordinate system attached with the plank which of the following equations represent trajectory of instantaneous centre of rotation of the disc a If a wk then y x 2 2a x 2a 22 x 2a w x 2a b If a wk then y c If ck then y d If wk then y and x 0 and x 0 and x 0 and x 0

Two wooden discs one with radius 2cm and mass 1kg and the other with radius 4cm and mass 2kg are welded together coaxially and mounted on a frictionless axis through their common centre A light string is wrapped around the edge of the smaller disc and a 3kg block is suspended from the free end of the string The acceleration of the block after it is released is in ms

A constant force acting at the centre of a uniform disc of radius r is always perpendicular to the plane of the disc The disc can rotate about a chord at a distance x from the centre of the disc For what value of x will the angular acceleration of the disc be maximum 75 Alco

Which of the following facts about the complex Cr NH3 Cl is wrong 1 The complex is an outer orbital complex 2 The complex gives white precipitate with silver nitrate solution 3 The complex involves d sp hybridisation and is octahedral in shape 4 The complex is paramagnetic

Two circular loops A and B of radii R and 2R respectively are made of the similar wire Their moments of inertia about the axis passing through the centre of perpendicular to their plane are I and I respectively The ratio A 1 2 1 3 1 2 IA IB 4 1 is

Q5 Two cylinders A and B weighing 100 N and 200 N respectively are connected by a rigid rod curved parallel to the smooth cylindrical surface shown in Fig Determine the angles a and that define the position of equilibrium A af B

n the figure is shown a pulley block system in which block of mass M s hanging on one side of pulley and on the other side a particle P of mass m is welded on pulley The moment of inertia of the pulley is and the system is in equilibrium when the particle is at an angle o from the vertical If the system is slightly disturbed from its equilibrium position find the time period of its oscillations a 2 C 2n RM m 1 R mg cos o RM m 1 R 2 mg cos o b T d 1 RM m 2 mg cos o RM m 1 R macos 1 R M

Moment of inertia of a sphere about its diameter is MR2 What is its moment of inertia about an axis perpendicular to point of intersection of two diameters Question Type Single Correct Type 1 2 MR 5 MR

A sphere of mass m is given some angular velocity about a horizontal axis through the center and gently placed on a plank of mass m The coefficient of friction between the two is The plank rests on a smooth horizontal surface The intial acceleration of the sphere relative to the plank will be m g 7 5 g 2 g

c Both will reach at the same time d None of the above 24 A solid cylinder rolls down an inclined plane of height 3 m and reaches the bottom of plane with angular velocity of 2 2rad The radius of cylinder must be take g 10 ms 2 a 5 cm c 10 cm b 0 5 cm d 7 5 m 28

A uniform semi circular ring of radius R 5m and mass m is free to rotate in vertical plane about fixed horizontal axis passing through A as shown in the figure The angular acceleration of ring immediately after it is released from rest from the position shown is in rad sec Solution Correct Answer 1 PDF

The system in the figure is in equilibrium A concrete block of mass 228 kg hangs from the end of the uniform strut of mass 40 6 kg For angles 21 2 and 9 63 1 find a the tension T in the cable and the b horizontal and c vertical components of the force on the strut from the hinge a Number b Number Ta Number Units Units Unite Strut Z 0 Hinge

Hence proved Ex 7 A heavy particle slides under gravity down the inside of a smooth circular tube held in the vertical plane It starts from the highest point with a velocity 2 ga where a is the radius of the circle Prove that when in the subsequent motion the vertical component of its acceleration is a maximum the pressure on the curve is equal to twice the weight of the particle teater and face and r

r 11 e the water level comes up to a height of 6 cm What will be the height of the centre of gravity of the cylinder containing 15 cm water Miscellaneous 10 A uniform straight rod of mass 50 kg and length 4 m is to be supported on two supports equidistant from the respective ends What can be the maximum distance of the supports so that a 30 kg counterpoising weight can be kept in equilibrium 1 25 m at any point on the rod 11 A bridge of mass 10 t and length 50 m is supported at its ends by two pillars What weight do the pillars sustain when a lorry of mass 4 t is 10 m away from the first pillar 8 04 x 104 N 5 68 104 N marks 3 or 4 PROBLEM SET 11 Based on Centre of Mass A circular hole of diameter 10 cm is punched in a uniform cir

Illustration 2 30 The top in the figure has a moment of inertia equal to 4 00 10 kgm and is initially at rest It is free to rotate about the stationary axis 44 A string wrapped around a peg along the axis of the top is pulled in such a manner as to maintain a constant tension of 5 57 N If the string does not slip while it is unwound from the peg what is the angular speed of the top after 80 0 CM of string has been pulled off the per

Starting from rest a particle rotates in a circle of radius R 2m with an T angular acceleration a rad s The 4 magnitude of a average velocity of the particle over the time it rotates quarter circle is

Q3 What are the necessary conditions for equilibrium of the object shown in Figure If F 10N F 15N F 5N and 1 1m Find the angle 8 which makes this beam in equilibrium torques about an axis through point O 10 points R

length a is kept on a rough horizontal surface A horizontal force P is acting on the block as shown in the figure If the block is neither sliding nor slipping then which one is incorrect F G H O A B Torque of weight about the centre of mass of the block is zero Torque of normal applied by the surface about the centre of mass on the block is non zero Normal force must pass through the edge AB Torque applied by friction force about centre of mass of the cube is non zero

Que 16 A string is wound around a hollow cylinder of mass 5 kg and radius 0 5 m If the string is now pulled with a horizontal force of 40 N and the cylinder is rolling without slipping on a horizontal surface see figure then the angular acceleration of the cylinder will be Neglect the mass and thickness of the string 12 rad s 2 16 rad s 2 10 rad s 2 J4 40 40 N

A uniform thin stick of length and mass m is held horizontally with its end B hinged at a point B on the edge of a table Point A is suddenly released The acceleration of the centre of mass of the stick at the time of release is AIPMT Mains 2007 A 3 49 If the earth ir B 3 79 D 6 N 2 C r g D 7 9 B

Que 10 The arrangement shows a solid cylinder of radius R placed between two planks There is no slipping at rough surfaces The planks are given a horizontal constant velocity as shown The angular velocity of the cylinder is ve 5V 4R 2V 3R 4V Rough

5 A coin runs on a horizontal plane without slipping What fraction of total energy K E is rotational Answer all questions Each carries 4 mark 6 A rotational K F of a particle rotating about a certain avis is 161 Coleulato

A uniform rod AB of length L and mass M is lying on a smooth table A small particle of mass m strikes the rod with velocity V at point C at a distance from the centre O The particle comes to rest after collision If the value of O so that the point A of the rod remains stationary just after the collision is then find n mV

100 Which of the following statements is not correct a During rolling the instantaneous speed of point of contact is zero 6 b During rolling the instantaneous acceleration of the point of contact is zero c For perfect rolling motion work done again friction is zero d A wheel moving down a perfectly frictionles inclined plane will slip but not roll on the plane

Which of the following is true about t angluar momentum of a cylinder rolling down slope without slipping 1 Its magnitude changes but the directic remains same 2 both magnitude and direction change 3 only the direction change

A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 6 50 m s when it starts up a ramp that makes an angle of 35 0 with the horizontal What is the speed of the sphere after it has rolled 3 00 m up the ramp measured along the surface of the ramp OA 3 70 m s OB 3 53 m s OC8 52 m s D 2 31 m s OE 4 26 m s

A disc of radius a and mass m rests between two light rods which are smoothly hinged together at point O with their ends A and B resting on a smooth table and are maintained in equilibrium by string AB as shown in the figure Choose the correct option s B The magnitude of normal force acting on the rod at point A is C The tension in the string AB is Aa mg A The magnitude of normal force acting on the rod at point A is 2 mg 2 mg D The tension in the string AB is 2 a cota sec a C OA OB C a tan a cos ec a B mg 2 cos a