Rotation Questions and Answers

A disc of mass m and radius R is rotating with angular velocity wo and is kept on a rough surface such that the plane of the disc is in the plane of surface and axis is vertical Coefficient of friction is u Choose the correct variations to is the time it takes before it stops T torque w angular velocity and 8 angular displacement AS Ro e am gez aaz uz za agiz cucai chi da adg an am H Gefuz 71 adu quic 1 ast ukada c to 3AH GA SH ug fau qu a94 1 dd 3f w un a A B C D mg R 3 3 3 0 30 R 8 g to 00 to Correct Answer 300R 2 g 3000R 4 g 30 R 0

A square wire frame of linear mass density 1kg m side length L 1m carrying current of 2A with its plane in X Y plane A uniform magnetic field B 2T is directed along y axis Find initial angular acceleration of frame in rad sec

8 A rigid equilateral triangular frame made of three identical thin rods mass m length is f to rotate smoothly in vertical plane Frame is hinged at one of its vertices H Frame is releas from rest from the position shown in figure then select correct atternative s He 3 A Net initial torque about point H is 2 3 12 mgl B Initial angular acceleration of the frame is g l C Initial force of hinge on the frame is 3 mg D Initial force of hinge on the frame is 3 mg horizontal D

questions will be considered for marking first 10 attempted A disc of radius 0 1 m rolls without sliding on a horizontal surface with a velocity of 6 m s It then ascends a smooth continuous track as shown in figure The height up to which it will ascend is g 10 ms 1 2 4 m 2 7 m 6m s Q 2 0 9 m 4 1 8 m ed from

Question No 7 Single Correct A The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its one end perpendicular to its length The relation between its length L and radius R is B L 2R L 3 ENGLE L 3R Marks 4 00

A particle of mass m is attached to an end of a uniform rod of mass M 2m and length which is suspended through its mid point by an inextensible string as shown Initially the rod is in horizontal position and at rest The system is released from this position Just after the release 2 mg f 2m 1 m s 12 www 12 2 23 g 2 69 51 01 31 6 41 2 6 6g A The angular acceleration of the system is 50 2g B The angular acceleration of the system is 5l M 12 C The Tension in the string is mg 5 2 D The Tension in the string is 5 mg m Zcom 0 mg1 m miz tim xing m Co 3 N CU 108 39 21

A body rotates about a fixed axis with an angular acceleration 1 rads 1 Through what angle does it rotate during the time in which its angular velocity increases from 5rads to 15rads

The moment of inertia of a solid cylinder about its own axis is the same as its moment of inertia about an axis passing through its one end and perpendicular to its length The relation between its length L and radius Ris L 2R A B C L 3 2 L 3R R

3 t Two monkey A B are of masses M and m respectively M m They are holding a rope which is passing through a stationary smooth pulley They moves on rope such that upward acceleration of B becomes double of downward acceleration of A then tension in the rope will be 1 3 4Mmg 2M m 3Mmg 2 M m 2 4 3Mmg M 2m 3Mmg M m blook with respect to block

Q9 A solid sphere of mass 4 0 kg and radius 0 12 m starts from rest at the top of a ramp inclined 15 and rolls to the bottom The upper end of the ramp is 1 2 m higher than the lower end What is the linear speed of the sphere when it reaches the bottom of the ramp Take g 9 8 m s O A 3 4 m s O B 4 1 m s O c 4 7 m s O D 2 4 m s

A rod of length and radius ris joined to a rod of length 1 2 and radius r 2 of same material The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of the twist angle at the joint will be A 0 4 B 0 2 C 50 6 D 80 9

26 u Four point mass each of mass m are connected at a corner of a square of side a by massless rods as shown in the figure x and y axis are in the plane of the system and z axis is perpendicular to the plane and passing through the centre of the square y A m a m A A Moment of inertia of the system about x axis is I ma B Moment of inertia of the system about y axis is I ma LC Moment of inertia of the system about the diagonal axis AA is IAA ma P Moment of inertia of the system about z axis is I ma 2 hm

20 A uniform solid cylinder of mass 4 kg radius r and height h 4r rests on a rough surface then choose INCORRECT option s F Br C h mA H 1 2 F is a variable force F F t where F 1 N s and t is in sec g 10m s A cylinder will topple over turn before sliding V B cylinder will slide before toppling X C cylinder will topple at time t 20 sec D cylinder will slide at time t 10 sec

A tractor is traveling 8 km h 5 mph while pulling a plow that exerts 20 kN 4500 lb of pu on the drawbar Calculate the linear drawbar power What are the standard rotational speeds of PTO of the word weight transfer 1374 in th

A solid non uniform sphere of mass m and radius R is released on smooth horizontal surface from the situation shown in the figure In given situation centre of mass C and geometric centre O R are on same horizontal line The distance OC is The moment of inertia about axis passing through C and perpendicular to the plane of the paper is Io is a and angular acceleration of the sphere is a Just after release relation between a a is A a a R aR 2 B a 69 0 C a 2aR MR 2 Acceleration of centre of mass D a 5 R 2

A uniform solid sphere of mass m and radius r rolls without slipping down a inclined plane inclined at an angle 45 to the horizontal Find the magnitude of frictional coefficient at which slipping is absent

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to the plane with angular velocity w Another disc of same mass but half the radius is gently placed over it coaxially The angular speed of the composite disc will be

Moment of inertia of a uniform rod of length L and mass M about an axis passing through a distance L from one end and perpendicular to its length is 2 1 3 ML 3 ML2 2 ML 12 7 ML

From a circular disc of disc of radius H adius H and masS R a small disc of radius is removed from the disc 2 as shown The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is 1 MR 3 R 2 R 13 8 MR

A uniform rod AB bent in the shape of a circular arc is free to rotate in vertical plane about a horizontal axis through the mid point of the rod If angular n acceleration of the rod just after the release from position shown is a 8 4b A Find n 0

A disc of radius 0 1 m rolls without sliding on a horizontal surface with a velocity of 6 m s It then ascends a smooth continuous track as shown in figure The height up to which it will ascend is g 10 m s 1 2 4 m 3 2 7 m 6m s C 2 0 9 m 4 1 8 m

made in a circular table as shown in the figure A small cubical block of mass 1 kg is placed inside a rough rectangular groove The table starts rotating with angular acceleration 1 rad sec in a horizontal plane about its axis The time is 10 K sec after which the block will start motion with respect to table Find the value of K Take g 10 m s2 Assume the size of block slightly smaller then the width of groove 3 cm 4 cm

string A mass m hangs with the help of a bearing The pulley has mass m and wrapped around a pulley on a frictionless radius R Assuming pulley to be a perfect uniform circular disc the acceleration of the mass m if the string does not slip on the pulley is c 9 30 d g a g b 39

1 From a disc of radius R and mass M a circular hole of diameter R whose rim passes through the centre is cut What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through the centre 1 15 MR2 32 2 13 MR 32 3 11 MR 32 4 9 MR 32

28 A circular disc is rolling on a horizontal plane Its 66 total kinetic energy is 300 J What is its translational K E 1 200 J 2 100 J 3 150 J 4 300 J 29 Figure shows the circular motion of a particle The radius of the circle the period sense of revolution and the initial position are indicated on the figure The simple harmonic motion of the x projection of the radius vector of the rotating particle P is RAJKOT CENTER P t 0 B X

3 A bar of cross sectional area A is subjected two equal and opposite tensile forces at its ends as shown in figure Consider a plane BB making an angle 0 with the length F4 B B F The ratio of tensile stress to the shearing stress on the plane BB is 1 tan A 2 sec 0

A disc having a groove along the diameter is rotating about its own axis passing through the centre of mass and perpendicular to its plane Two masses m and m are connected with the spring of force constant k and the combination is placed at the centre of the disc Distance of centre of mass of the two blocks from the axis of rotation will be A zero B C m m R m m D m m R m m m R m R m m Imon 3

4 2x A solid sphere of mass m and radius R is rotating 44 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 2 3 1 3 2 3 4 1 5 4 2x qui a fo te fufis m a a f qui fac si EE 3 1 1 4 2 3 1 3 2 3 4 1 5

Disc A of mass m radius r and disc B of mass 2m radius r are placed on horizontal smooth floor Disc A is given angular velocity about its stationary vertical central axis and disc B is projected with horizontal velocity v without rotation for a head on collision to occur between them If collision is perfectly inelastic and slipping between disc ceases in the end of collision then after collision A Angular speed of disc A is 500 9 3v C speed of centre of disc B is 2 B Angular speed of disc B is D speed of center of disc A is 400 9 3v G 2

The moment of inertia of a thin sheet of mass M of the given shape about the specified axis is A 2 M B 5 Ma C Ma D Ma

Two thin discs each of mass Mand radius rare attached to form a rigid body The moment of inertia of the system about an axis passing through the diameter of the disc and in the plane of the disc as shown in figure will be B 7Mr 2 Mr 2 9Mr A

A lever 11 m long is used to lift a load of 2000 N The distance from the load to the fulcrum is 1 meter What is the minimum force needed to lift the load Hint draw the lever and the point of fulcrum about 1800 N about 2 N about 20 N about 200 N

Physics Question No 24 Question Palette A ring of mass m 1 kg and radius R 1 25 m is kept on a rough horizontal ground A small body of mass m is struck to the top of the ring When it was given a slight push forward the ring started rolling purely on the ground What is the maximum speed of the centre of the ring in ms

100 mm C 240 mm 300 mm 200 mm B 1 12 60 pts A force with a magnitude of P 1170 N acts on the structure

No 22 View In English A disk and a sphere of same radius but different massos roll off on two inclined planes of the same altitude and length Which one of the two objects gets to the bottom of the plane first 1 Disk Sphere Both reach at the same time Depends on their masses

A uniform ring of radius r 1 metre and mass m is rolling without slipping with velocity V towards a step of height b 0 9 m on a horizontal surface Assume that ring does not rebound and no slipping occurs at point of contact when the ring rolls up If the minimum velocity needed for ring to roll 4x the step is m s find x 1 1 up D A 0 9m

A wheel of radius R 2m performs pure rolling on a rough horizontal surface with speed v 10 m s In the figure shown angle 0 is angular position of point P on wheel from where dirt fell from wheel reaches the maximum height from ground Find the value of sec0 take g 10 m s P

10 An electric field line emerges from a positive point charge q at angle a to the straight line connecting it to a negative point charge 2q as shown in figure At what angle will the field line enter the charge 2q 1 a 3 sin 1 94 sin 2 2Sin 1 2 4 sin 1 2 sin a 2 1 Explokking sin 2 2 2 a ro 24

In the solution of this question the met torque is taken 0 and sum up th e two torquesa so calculated the dist ance by the equation but as the 2 for ces are acting in the opposite edges so they should be substracted from one another 41 42 Two like parallel forces 20 N and 30 N act at the ends A and B of a rod 1 5 m long The resultant of the forces will act at the point 1 90 cm from A 2 75 cm from B 3 20 cm from B

4 changed in unpredicted manner The instantaneous angular position of a 30 point on a rotating wheel is given by the equation 0 t 2t 6t The torque on the wheel becomes zero at 1 t 1s 3 t 0 25 s 2 t 0 5 s 4 t 2s 4 fazef quia and gu feu fazeft farg uz arcerfora af feef 8 t 21 61 for a 1 t 1s 3 t 0 25s few 2 t 0 5 s 4 t 2s

A small mass attached to a string rotates on a rictionless table top as shown If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 the kinetic energy of the mass will a decrease by a factor of 2 b remain constant c increase by a factor of 2 d increase by a factor of 4 Mains 201

A metal rod AB of length L rotates with a constant angular velocity w about an axis passing through O and normal to its length The magnitude of emf induced between ends A and B in the absence of mL 2 external magnetic field is ke and e is charge of electron Find k where mis mass B

In the figure shown C is a fixed wedge A block B is kept on the inclined surface of the wedge C Another block A is inserted in a slot in the block B as shown in figure A light inextensible string passes over a light pulley which is fixed to the block B through a light rod One end of the string is fixed and other end of the string is fixed to A S is a fixed support on the wedge All the surfaces are smooth Masses of A and B x are same Then the magnitude of acceleration of A is m s Then x 3 B 37 C S

1 3 rod of mass m and length is hanging at one end as shown in figure A bullet vertically of mass fired with velocity v strikes the rod in the middle and sticks to it then angular velocity of rod about hing just after being hit is shing 2K 3 3V 77 EN 2 F 6V 1

9 Online Mock Test Series for NEET 2020 A thin rod of length 3 and mass 3m is bent as shown in figure Then moment of inertia of the given structure about an axis passing through point O and perpendicular to the plane containing rod is 1 m 3 90 A 60 2 m

A disc of mass m is rolling on a horizontal surface with velocities as shown in figure A B C Bd T The kinetic energy with respect to point P on the disc is mv The kinetic energy with respect to point P on the disc is my The angular momentum with respect to point P 3mlfw 4

ere place aced on fixed rough horizontal surface is pulled horizontally by a force s shown in the figure If it undergoes pure rolling then the frictional force acting on sphere O is AUTO ash 253 1 P 2 352 F 2E

Two identical circular discs A and B each of mass m and radius R are placed horizontally on a smooth horizontal surface with their centres fixed to the surface and touching each other as shown Now an impulse Po is applied to the disc A as shown If there is no slipping between the discs the angular velocity of each disc will be A Po 2mR C Po mR B 2Po mR D Po 4mR Po A C B C C

2 A bracket is subjected to two forces as shown in figure 2 Determine a moment of 160 N force about point A b moment of 210 N force about point A and B A 160N 210NY 1m 0 4m Figure 2 B 0 7m

9 Consider a particle of unit mass being thrown with an initial velocity making an angle wit the horizontal ground What is the magnitude of the angular momentum of the particle about th point of projection at a time t after its projection while it is in flight A 2gt2v cos B gtr cos C 2gt2 sino