Rotation Questions and Answers

The moment of inertia of thin square plate ABCD of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is not equal to Given I I I3 and I respectively are the moments of inertia about axes 1 2 3 and 4 which are in the plane of the plate ABCD 1 1 1 2 3 D A 1 1 B 1 1 13 14 Iz C 1 13 D 1 1 1 14 Your Answer

A disc of mass m and radius R rotates centre of mass with constant angular speed w Its centre of mass moves with a constant velocity v parallel to the x axis as shown At an instant its centre of mass has the coordinates 1 b Its angular momentum about O at that instant is Moment of Inertia of disc about c o m c 1 mvb 3 w mvl 00 V X 2 w mvb 4 Lo myl

A uniform thin rod of length L is oscillating in vertical plane about a fixed horizontal axis passing through one of its end Frequency of small oscillations of the rod is Vo If bottom half of the stick were cut off then its new frequency would become 28 Vo VO 2v0 2V0

ALL the equivalent resistance between the points A and D Infinite ladde 1 100 A 220 2 3 30 2 4 40 2 C In the circuit sho 10 CA www 10 0 10 02 10 C www 10 03 www 10 0 10 0 www 10 0

A small ball of mass m and radius r 10 rolls without slipping along the track shown in the figure The radius of circular part of the track is R If the ball starts from rest at a height of 8R above the bottom the normal force on the ball at the point P is 8R A mg 100 3 Your Answer 100 10 mg B R 200 9 C mg Correct Answer P

A nonconducting ring of mass m and radius R is charged as shown The charged density i e charged per unit length is It is then placed on a rough nonconducting horizontal surface plane At time t 0 a uniform electric field E Ei is switched on and the ring start rolling without sliding Determine the friction force magnitude and direction acting on the ring when it start moving

If I is the moment of inertia of a solid body having a coefficient of linear expansion then the change in I correspondin to a small change in temperature AT is 1 qI AT 3 2 a IAT 2 a1 AT 4 3 a IAT

A solid cylinder of mass M and radius R rolls without 1 slipping down an inclined plane of length L and height h What is the speed of its centre of mass when the cylinder reaches its bottom A 2gh 4 C gh 3 B 3 gh D 4gh

When the 0 05 kg body is in the position shown the torsional spring at O is pretensioned so as to exert a 0 75 N m clockwise moment on the body Determine the force P required to break contact at C Complete solutions for including the effect of the weight Select one a 6 25 N b 5 N c 5 25 N d 6 N A 60 mm C 60 mm ke O 80 mm

d their lines of action are at equal The 30 N force P is applied perpendicular to the portion BC of the bent bar Determine the moment of P about point A P 30 N Select one a 36 4 N m CCW b 81 9 N m CW c 73 5 N m CCW d 54 7 N m CW C 1 6 m B A 1 6 m

A non uniform rod of length has linear mass density Aoz where Ao is a positive constant The rod is pivoted at point P and is free to rotate in the vertical plane without friction as shown in the figure below The rod is released at rest is the gravitational acceleration Find the speed of the bottom tip of the rod when it is in the vertical position O O O None N For 2gl 2gf 21 too M

Which of the following statement is incorrect Moment of inertia is independent of distribution of mass about rotational axis Moment of inertia depends on orientation and position of axis of rotation Moment of inertia is independent of angular velocity of rotating body Flywheel resists sudden increase or decrease of speed of vehicle

Two particles each of mass m and charge q are attached to the two ends of a light rigid rod of length 2 R The rod is rotated at constant angular speed about a perpendicular axis passing through its centre The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is TH 9 2m 2 9 m 3 24 m 44 9 70m

A body of mass M and radius of gyration K is rotating with angular velocity w 3t f rad s The torque acting on it at 1 1 s will be 4MK 5MK 2MK

Athin rod of length 2R is placed inside a smooth spherical shell of radius R The rod is vertical and i ends are in contact with the inner surface of the shell The rod is released from this position A Maximum speed of the mid point of the rod will be 3gR 2 2 B Angular velocity of the rod when it becomes horizontal is C At any moment all points of rod will have same speed D The maximum velocity of the ends of the rod will be 3gR 2 3g 2R

particles 1 and 2 are allowed to descend on the two frictionless chord OA and OB of vertical circle at the same instant from point O The ratio of the velocities of the particles 1 and 2 when they reach on the circumference will be OB is diameter 1 sin a 2 tan a 3 cos a 4 independent on A B

84 In the figure shown the rod is uniform and has a mass m length L The horizontal thread is conner rod at a point at a distance L 3 along the rod from lower end and angle between rod and wall is 60 V A In equilibrium tension in the thread is 3mg 2 B In equilibrium tension in the thread is 3 3mg 2 150 25 C The minimum value of friction coefficient between the lower end of rod and the vertical wall for the rod be in equilibrium is 2 3 3 D The maximum value of friction coefficient between the lower end of rod and the vertical wall for the

Calculate the moment of inertia of a disc of mass 0 4Kg and radius 0 12m about an axis passing through its center and at right angles to its plane What would be the moment of inertia if the axis passes through a point at a distance from the center equal to half the radius of the disc

For finding the moment of inertia of a d isc with radius R we assume that the di sc is made up of many small rings of m ass dm radius x and width dx But as x tends to R the mass of the small rings s hould increase i e dm should increase The small ring which is farther from ce ntre should have a higher dm as compa red to those which are closer to centre But we assume that dm is constant for integration Why do we assume that all small rings should have the same mass dm Scientifically it is not possible

A gyroscope spins with its tip on the ground and is spinning with negligible frictional resistance The disk of gyroscope has mass 0 3 kg and is spinning at 2 0 rev sec Its center of mass is 5 0 cm from the pivot and the radius of the disk is 5 0 cm What is the processional period of the gyroscope O 5 0 sec O 3 0 sec O2 0 sec O 2 5 sec

the figure shown a uniform disc of mass 2m and radius 12 is lying at rest on a smooth horizontal surface A particle A of mass m is connected to a light string of length whose other end is attached to the circumference of the disc Initially string is just taut and tangential to the disc and particle A is at rest In the same horizontal plane another particle B of same mass m moving with velocity vo perpendicular to string collides elastically with A Just after impact which of the following statements will be true IC 2mv2 5l mv2 A Tension in the string is C Tension in the string is B 2m A 111 B Acceleration of the centre of the disc is 50

A particle of mass m is thrown with speed vo at an angle 30 with horizontal The angular momentum about the point of projection when the particle is at the highest point of its trajectory Question Type Single Correct Type 1 2 3mv 2g 3mv 8g

7 Explain the linear velocity of a particle perform ing circular motion OR Derive the relation between the linear velocity and the angular velocity of a particle performing 2 marks circular motion

A person is riding a bicycle in vertical portion accelerating forward without slipping on a straight horizontal road What is are the direction s of the total force exerted by the road on front P and the IJSO Stage II 2014 rear Q wheel P

2 149 The minimum force F needed to push the two 50 kg cylinders up the incline is 200x Newton The force acts parallel to the plane and the coefficients of friction at contacting surfaces are as A 0 3 between cylinder A and ground B 0 25 between cylinder B and ground and c 0 between two cylinders The cylinder A can rotate about its axis without friction Find the value of x F 37 AB

A particle of mass m is attached to one end of the light inextensible string and other end of the string is fixed in vertical plane as shown Now 5 particle is given horizontal velocity u gl then which of the following 2 statement s is are correct U A The string makes angle with the downward vertical is 60 when acceleration of the particle is horizontal B The tension in string is 2 mg when acceleration of the particle is horizontal 3 C The speed of the particle is gl when acceleration of the particle is horizontal 2 D The particle will not complete the circle

Three identical spherical shells each of mass m and radius r are placed as shown in figure Consider an axis XX which is touching to two shells and passing through diameter of third shell Moment of inertia of the system consisting of these three spherical shells about XX axis is 1 3 mr 3 4 mr X 16 mr mr

7 A rod of weight W is supported by two parallel l edges A and B and is in equilibrium in a horizo position The knives are at a distance d from other The centre of mass of the rod is at dista x from A The normal reaction on A is 1 3 Wd X W d x d 2 4 W d x X Wx d

Q 142 Just after release of rod as shown on smooth horizontal track Find the ratio acceleration of point A and a is angular acceleration of rod just after release vertical 60 60 ammun smooth massless string 60 B uniform rod 2a la where a

When a mass is rotating in a plane about a fixed point its angular momentum is directed along 1 the radius 85 2 the tangent to the orbit 3 a line perpendicular to the plane of rotation 4 the line making an angle of 45 to the plane of rotation

A 10 kg solid sphere of radius r 0 8 m is rolling without slipping on a horizontal rough surface with 8 m s The force applied by the right half of the sphere on the left half is 30x Newton Find the value of x 8 m s

An elevator initially at rest supported by a cabl passes over a pulley of radius 0 4 m It is accelerater upwards with 0 6 m s Find number of rotation made by pulley during 10s 1 23 88 3 5 97 2 11 94 4 8 96

28 A solid sphere of mass m and radius R is rotating about its diameter A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere The ratio of their kinetic energies of rotation Esphere Ecylinder will be 1 1 4 3 2 3 2 3 1 4 1 5

A uniform rod AB of length and mass m is free to rotate about A The rod is released from rest in the horizontal position Given that the moment of inertia of the rod about A is me acceleration of the rod will be 3 1 3g 20 3 mg A l B 2 the initial angular AIPMT 2007 2g 3l 3 4 gl

An automobile moves on a road with a spee 54 km h The radius of its wheels is 0 45 m the moment of inertia of the wheel about its of rotation is 3 kg m If the vehicle is broug rest in 15s the magnitude of average fo transmitted by its brakes to wheel is 1 2 86 kg m s 2 6 66 kg m 3 8 58 kg m s 4 10 86 kq m

solid sphere placed on rough horizontal surface is given velocity vo as shown at t 0 If coefficient of riction is then time to at which it rolls without slipping is 20 Find n nug 0 0 Vo

Find the maximum height upto which disc can reach on the incline plane when given velocity v horizontally disc is performing pure rolling motion Ohmax Ohmax Ohmax 3v 4g 2v 9 4v 3g To D

If you apply the same 50 N force at the halfway point at 12 cm point instead of the 24 cm point between the center of the bolt and the current position how much is the torque is reduced compared with t torque at the 24 cm point a fraction of the onginal torque between 0 and 1 0 See the figure below BAS 24 cm 50 N

Q 16 Why the diver stretches her arm and leg while touching the water a to increase her moment of inertia b d c to relax her body to decrease her moment of inerti to increase her velocity

Three parallel bolting forces act on the rim of the circular cover plate as shown in Fig 3 b Determine the magnitude nature and point of application of the resultant force with respect to origin O 6 200 N B 300 N A 0 Z 150 N 450 0 8 m C

The magnitude of acceleration of a point on the wheel s rim at f 1 s whose radius is 2 m anc is spinning with angular velocity to that varies with time as 10 f rad s is 1 40 26 m s 2 40 m s 3 Zero dw at

If the radius of the earth suddenly contracts to one third of its present value then the duration of the day will be approx Mass of earth remains constant 1 24 hours 2 8 hours

A hollow sphere is moving with linear velocity and angular velocity as shown in figure The time after which pure rolling starts is Question Type Single Correct Type 1 2 3 A 2v 3 g 4v 7 g 4v 5 g 0 3v R 5v

A wheel of radius R rolls on the ground with a uniform velocity v The relative acceleration of topmost point of the wheel with respect to the bottommost point is 1 3 12 R 12 2 4 21 R 4v F

A cylinder of radius R 20 cm is moving between two planks as shown in figure There is no slipping at any point The angular speed of cylinde is 10 m s 20 rad s O 10 rad s 8 rad s O 40 rad s 2 m s phy 08

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its centre with a uniform angular speed 2 rads The radius of the disc is 50 cm Find the minimum coefficient of friction between disc and coin so that the coin does not slip g 10ms 2 1 0 1 2 0 2 3 0 3 4 0 4

Question Number 01 to 15 Only one option is correct A particle starts moving in a circular path of radius R with an initial angular speed rad s and angular retardation radian see The acceleration of the particle will be directed along its velocity after time D it is impossible A 000 X a 2a

A small spherical metal ball of radius r is lying at the bottom of a stationary container containing liquid of density p as shown in the figure Po is atmospheric pressure Force exerted by liquid on the upper hemispherical part of the sphere is 4r 1 Question Type Single Correct Type AC r 3 3Po 7rpg

horizontal plane with constant speed Its angular momentum about hinge X l m 1 Conserved 2 Only direction is conserved not the magnitude 3 Only magnitude is conserved not the direction 4 Neither magnitude nor direction

A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R as shown in the figure The moment of inertia of this lamina about axes passing through O and P is I and Ip respectively Both these axes are perpendicular to the plane of Ip the lamina The ratio to the nearest integer is Io 2R 2R P