Rotation Questions and Answers

40 A uniform rod of length I is pivoted at point A It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in figure Impulse delivered by pivot is zero if x is equal to 1 a 3 b d 3 3 4 X A

The moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through one end is I The same rod is bent into a ring and its moment of inertia about the diameter is I The ratio 4 w 5 4T B is 1 87 3 ST C 3 D 87 5

A composite rod of length 2L and mass 3m has half of its section made of material of uniform densityP and other half of uniform density 2p Choose the correct statement L String 1 0 L P 2p String 2 5g The angular acceleration when string 1 is cut is 61 7g The angular acceleration when string 2 is cut is 10L 11 The tension in string just after string 1 is cut s 12 11 The tension in string just after string 2 is cut in mg MATH SEC II

rod of mass M is released from position shown in figure The surface of sphere is smooth radius of sphere is Im and accelera V3 ue to gravity is 10m s he maximum speed of center of mass is V in Sl units The value of V is 60

A thin uniform rod of length is released from rest from the position shown in the figure All contact surfaces are smooth If the initial angular acceleration of the rod is k 3g 20 Find the value of k 60 30

A crooked pulley of mass M 8kg made of a uniform disk of radius R 1 m is mis manufactured to have its hinge off its center by a distance h 1 3 cm h R An inextensible string connected to two masses m 1 kg passes over the pulley as shown Initially the center of mass C of the pulley is at the same horizontal level as X axis The system is released from rest in the position shown Assume that slipping does not take place anywhere and there is no friction at the hinge Find the magnitude of inverse of initial angular acceleration of the pulley in SI units Take appropriate approximation Bm M hy HI R C X 8 0 mA

The densities of two solid spheres A and B of the same radii R vary with radial distance r as PA r K R and PB r K respectiv k where k is a constant The moments of inertia of the individual spheres about axes passing through their centres are lA and n the value of n is 10 respectively If B IA

A uniform rod has mass m 2 kg and length 13m One end of the rod is pulled with a constant velocity of vo 34 m s along frictionless horizontal floor in the negative x direction The other end is moving along a parabolic fixed curve The equation of the parabola is x 20y Find the angular velocity of the rod in rad s when the end point B is at 10 5 y axis x 20y A 0 0 B 10 5 X axis

Consider a conical pendulum in which a small sphere of mass m revolves in uniform circular motion in horizontal plane as shown in figure Identify the incorrect option Suwww AY Om mg 1 The torque of force mg about point O as well as about axis SO is zero 2 The torque of tension T of string about axis SO is zero 3 The torque of tension T of string about point S is zero 4 The torque of force mg about axis SO is zero but about point S is mgl sine k

Three point masses each of mass 2 kg are placed at the corners of an equilateral triangle of side 3m Then the moment of inertia of th system about an axis passing along one side of the triangle is In Kg m

This section contains 20 questions Each question has 4 options for correct answer Multiple Choice Questions MCQs Only one option is correct For each question marks will be awarded as follows Full Marks 4 If correct answer is selected Zero Marks 0 If none of the option is selected Negative Marks 1 If wrong option is selected Eight point objects each of mass M are at the vertices of a rigid massless framework in the form of a cube each side is of length a What is the moment of inertia of this arrangement about an axis passing through one edge of the cube O 4Ma O 6Ma 8Ma

Negative Marks 1 If wrong option is selected Nine point mass m are arranged in an double cone system as shown in diagram Radius of each cone is R and height of each cone H The moment of inertia about the x axis passing through the common vertex is im L 8 mH 8 m H R 8 mH 4 mR None of these me m m m im m m m

A Rotating Tilted Rod Figure shows a thin uniform rod AB of mass m and length rotating about the vertical axis 00 at angular velocity Find the torque of centrifugal forces acting on rod about its mid point c in the frame of reference rotating at angular speed attached to axis 00

A uniform body of mass M of radius R has a small mass m attached at edge as shown in the figure M A m The system is placed on a perfectly rough horizontal surface such that mass m is at the same horizontal level as the centre of body It is assumed that there is no slipping at point A If IA is the moment of the inertia of combined system about point of contact A then the normal reaction at point A just after the system is released from rest is M 6 kg m 2 kg lA 4 kg m R 1 m g 10 m s

A disc is given an initial angular velocity and placed on rough horizontal surface as shown The quantities which will not depend on the coefficient of friction is are A The time until rolling begins B The displacement of centre of mass of the disc until rolling begins C The velocity when rolling begins D Angular velocity when rolling begins

1 a Three objects a solid cylinder a solid sphere and a hollow sphere all have the same mass of 3 2 kg and radius of 15 cm rotating about the axes going through their centers Rank the moment of inertia in descending order for different shapes 1 b If all mentioned objects with different shapes in question a are rolled down from the same ramp which one will reach first to the ground Also rank their translational speeds greatest first Explain

SV A solid uniform ball of mass m and radius R collides elastically with a rough fixed inclined surface as shown Velocity and angular velocity of ball just before collision are V and Choose R correct option s A Ifu KET C Ifp then the velocity of ball just after collision is vertically upwards B If u then the velocity of ball just after collision is horizontal leftwards Rough p 3 then angular velocity after collision is 4 2Vo R 3 D If then velocity of ball after collision is V

c A particle of mass 2 00 kg located at position 7 2 3 2k m with respect to the axis passing through the origin experiences a force of F 5 4 8k N 1 calculate the torque acting on the particle about the origin Specify the direction of torque 2

An uniform rod of length L cross sectional area A and Young s modulus Y has negligible self weight One end of the rod is hinged and a particle of mass m is attached to the other end The system is released from rest from the horizontal position The extension in the length of the rod when the particle is at the lowest point is 1 3 mgL YA 3mgL YA 2 4 2mgL YA 4mgL YA

A ring a solid sphere and a thin disc of different masses rotate with same rotational KE Equal torques are applied to stop them Which one will make least number of revolutions before coming to rest Ring Disc Solid sphere

2 Two equal and opposite forces are appl tangentially to a uniform disc of mass M and radius R as shown in the figure If the disc is pivoted at its centre and free to rotate in its plane the angular acceleration of the disc is 1 F MR R 2 2F 3MR F

A disc of mass 2 kg is rotating with angular velocity 30 rev 1 2 kg 30 rev sec tra m qu sec What is angular velocity if a mass of 0 25 kg is put on aff0 25 kg periphery of the disc 1 24 rev sec 2 36 rev sec 3 15 rev sec 4 26 rev sec entity an 1 24 rev sec 2 36 rev sec 3 15 rev sec 4 26 rev sec

Read the paragraph carefully and answer the following questions In a gravity free space a hollow cylinder of radius 4R and mass M is being rotated by a constant angular velocity clockwise w r t an inertial frame of reference Another hollow cylinder of radius R and mass m is rotating inside this cylinder such that it touches the inner surface of larger cylinder without slipping and its centre of mass appears stationary from inertial frame Dynamic friction coefficient between cylinders is u If the normal reaction between cylinders is denoted by N answer the following questions 37 38 39 What is the angular velocity of smaller cylinder A w 3 C 4 What is the value of N A m 4R w C m 3R A m 4 C m B 30 D 30 4 3R 3w 4 v 3R B m R 40 D zero A small tangential velocity v is given to the smaller cylinder towards right What will be N Once the steady state is achieved V 16R B m V 12R 4R D zero R

A wheel of radius 20 cm has forces applied to it as shown in the figure The net torque produced by the forces 4N at A 8N at B 6N at C and 9N at D at angles indicated is 8N 130 4N 90 A 20cm 90 L C 6N 1 5 4 N m anticlockwise 2 1 80 N m clockwise 3 2 0 N m clockwise 4 5 4 N m clockwis D V9N

A uniform thin rod ABC of mass M and length is placed vertically on a rough horizontal surface The coefficient of kinetic friction between the rod and the surface is u A force F sufficient for sliding is applied on the rod at point B at distance 1 3 below centre of the rod as shown in figure The initial acceleration of point A is g M 1 3 C F

A uniform rod of mass M and length 1 is dropped on horizontal smooth surface from the position shown What is the velocity in m s of centre of mass of rod immediately after elastic collision g 10 ms h 9 8m 60 TTT Correct Answer

A small ball is kept inside a smooth tube of length L 2 m at r and then the Tube is rotated in horizontal plane with constant angular speed 3 rad s about vertical axis passing through one end of tube The speed of ball when it comes out of tube is n m s Find the value of n

Consider a uniform rod of mass M 4m and length pivoted about its centre A mass mi moving with velocity v making angle to T 4 the rod s long axis collides with one end of the rod and sticks to it The angular speed of the rod mass system just after the collision is 3 3 v 7 27 317 2 3 2 v 7 3v 76

Consider a uniform circular disc M R having a point mass M at its circumference Disc is rolling over a rough horizontal surface consider the arrangement shown in the position At this position an is the acceleration of centre of disc wo and a are the angular velocity and angular acceleration of disc at this instant Now choose the correct option s Disk M R 80 2a If o be forward be forward M direction of frictional force will direction of frictional force will XN normal reaction from ground 2 Mg N normal reaction from ground 2 Mg

10 A uniform rod AB of mass m and length l is at rest on a smooth horizontal surface An impulse P is applied to the end B The time taken by the rod to turn through a right angle is A T me ml B 12 P P C 2 me D 2 me

The axle of a uniform cylinder with mass m and radius R is connected to a spring with spring constant k as shown in the Fig A horizontal board with mass m rests on top of the cylinder and the board also rests on top of a frictionless support near its left end The system is slightly displaced from equilibrium There is no slipping between the cylinder and the board or between the cylinder and the ground The angular frequency of the oscillatory motion is p The value of 11p m k is frictionless m m C eeeeeeee k eeeee

Four thin rods each of same mass M and same length form a square as shown in figure Radius of gyration of this system about an axis through centre O and lying in its plane is 1 13 V24 13 l 2 13 6 l

The sphere shown in figure lies on a rough plane when a particle of mass m traveling at a speed vo collides and sticks with it If the line of motion of the particle is it a distance h above the plane find a the linear speed of the combined system just after the collision b the angular speed of the system about the center of the sphere just after the collision and c the value of h for which the sphere starts pure rolling on the plane Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere T h m

A solid cylinder mass m radius r a hollow cylinder mass m radius 2r a solid sphere mass m radius 3r and a hollow sphere mass m radius 4r are released at the top of an incline Assuming that friction is just sufficient for rolling of hollow sphere Which of these will reach bottom of the incline simultaneously 1 Solid cylinder and hollow sphere 2 Hollow sphere and hollow cylinder 3 Solid sphere and solid cylinder 4 Hollow cylinder and solid sphere

Two identical rigid rods each of mass 1kg length 3m are moving opposite to each other without rotation on a smooth horizontal table as shown For what maximum value of x after rounding off to two places of decimal the direction of motion of each rod would not change after collision irrespective of the type of collision Assume no sticking Also assume that Normal reaction between rods is essentially acting at the midpoint of parts of the rod which are in contact L X L

A th triangular sheet of mass M has sides AB BC L What is its moment of inertia about axis AC lying in plane of sheet 1 ML B 2 2ML 3 C ML 0 ML

If the centre of gravity of a metre scale of mass 80 g lies at the 45 cm mark then which one of the following diagrams will show the balanced position of the scale 1 2 3 4 0 0 50 60 Fulcrum 50 60 Fulcrum 50 60 50 Fulcrum 60 100 40 gf 100 45 gf 100 30 gf 100

Three uniform thin rods each of mass 1 kg and length 3 m are placed along three co ordinate axes with one end at the origin The moment of inertia of the system about X axis is B 3 kg m D 1 kg m 2 2 A 2 kg m 2 C 0 75 kg m

1 o tan 0 4 40 tan 0 1 2440 tan 0 A small mass slides down an inclined plane of inclination the horizontal the coefficient of friction is ox where x is the distance traveled by the mass before it stops is

A uniform pole is attached to a vertical wall by a frictionless pivot The pole is held horizontal by a vertical mass less cable attached to the ceiling as shown in the diagram Considering torques on the pole about the axis of the pivot which of the statement is CORRECT pivot cable

A uniform wire is bent in form as shown in the figure It is suspended from the point from where curved portion starts curved portion is semicircular Find value of a in terms of r such that straight portion remains horizontal r

A horizontal groove AB is made inside a uniform circular disk m R hinged at its topmost point in vertical plane as shown An insect of mass m starts its motion from point A to B in such a way so that disk always remain in rotational equilibrium then B www m R A Options Time taken by insect to reach at other end of groove is g Time taken by insect to reach at other end of groove is 2 g Maximum force exerted by insect on disk is mg Maximum force exerted by insect on disk is ma 5

A rod of length 2L is inclined at an angle 8 to the horizontal It falls without rotating from a certain height H It hits a horizontal table surface initially on the left hand end and then on the right hand end The impact of the rod is elastic and friction can be ignored When the rod hits at right hand end it is again found to make angle 9 with the table surface Calculate the relationship between H and 8 21

Two circular plates of radius 0 1 m are used to form a parallel plate capacitor If displacement current between the plates is 2n amp then find magnetic field produced by displacement current at 4cm from the axis of the plates 1 4 T 2 2 T 3 8 T 4 u T

on a plane horizontal mirror with constant angular velocity as shown in figure P is contact point and line PQ makes an angle with vertical at given instant The velocity of image of point Q with respect to itself would be A 1 2 2 2ro cose 2 2rm sine cose

8 The moment of inertia of a uniform solid disc of mass M and radius R about an axis normal to the disk and passing through its center is MR What is the moment of inertia of the same disc about an axis lying in its plane and tangent to it as shown in the figure 2 A MR 4 B 3MR2 C MR D SMR2 R

A force F 10N is act at the upper end of a solid sphere mass of the sphere is m 5kg and its radius is 1m then I find transational acceleration find find frictional force Assume that there is no slipping m 5kg r 1m T O

A horizontal square platform of mass 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 1m A B A B Angular velocity of platform when the person is at A is 6 rad s 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 remains constant as the person goes from A to B C D The body is rotated in the vertical plane by means of a thread of

5 A particle of mass m is suspended from point O and undergoes circular motion in horizontal plane as conical pendulum as shown in figure www on C A Angular momentum of particle about point of suspension does not remains constant B Angular momentum of particle about centre of circle remains constant 2mg tan 0 C Average force during half rotation is TU D Average torque about axis OC during half rotation is zero

A small particle of mass m is attached at B to a hoop of mass m and radius r whole system is placed on the rough horizontal ground The system is released from rest when B is directly above A and rolls without slipping Find the angular acceleration of the system at the instant when AB becomes horizontal as shown in the figure E