Rotation Questions and Answers

8 A body is in pure rotation The linear speed v of a particle the distance r of the particle from the axis and the angular velocity wo of the body are related a e doinw V Thus r Xa a w x 1 r c 0 igale t pritiw allo sonil od eam to everige blloz Al b writo enla d is independent of r w d 0 nie 0 ito

4 it moves in a straight line A point P moves in counter clockwise direction on a circular path as shown in the figure The movement of P is such that it sweeps out a length s t 5 where s is in metres and t is in seconds The radius of the path is 20 m The acceleration AIEEE 2010 of P when t 2 s is nearly Ex B 20 m P x y A lai 4 14 m s

7 A diver in a swimming pool bends his head before diving because it a decreases his moment of inertia b decreases his angular velocity e increases his moment of inertia d decreases his linear velocity

A ring of mass m and radius R is acted upon by a force F as shown in the figure There is sufficient friction between the ring and the ground The force of friction force necessary for pure rolling is Ia F m R R MR a F 1 5 2 forward R 2 F 3 F fk cam Rf Ia forward

21 A solid cylinder is rolling without slippily velocity of its centre of mass v and angular velocity about its centre of mass won a horizontal frictionless surface as shown in figure If it collides with a frictionless vertical wall X then after collision its velocity and angular velocity respectively become I 1 IN 3 N 22 00 G X 2 V w

A solid cylinder of mass 50 kg and radius 0 5 m is free to rotate about the horizontal axis A massless string is wound round the cylinder with one end attached to it and other hanging freely Tension in the string required to produce an angular acceleration of 2 2 revolutions sis A 25 N C 78 5 N B D AIPMT 2014 50 N 157 N

Example 11 3 A sphere of aluminium of 0 047 kg placed for sufficient time in a vessel containing boiling water so that the sphere is at 100 C It is then immediately transfered to 0 14 kg copper calorimeter containing 0 25 kg of water at 20 C The temperature of water rises and attains a steady state at 23 C Calculate the specific heat capacity of aluminium

186 A rod of mass m and length 2R is attached to a circular ring of mass m and radius Ralong its vertical diameter as shown Horizontal force F is applied at top Friction is sufficient for pure rolling then friction force acting on the ring at the instant shown is N st Mgr 2 Ring m R Rod m F 20 N FR n

A 15 kg uniform disk of radius R 0 25 m has a string wrapped around it and a m 3 8 kg weight is hanging on string The system of the weight and disk is released from rest 1 When the 3 8 kg weight is moving with a speed of 1 4 m s what is the kinetic energy of the entire system K E 20 235 m Your submissions 20 235 X Computed value 20 235 Feedback Ann Submit 2 If the system started from rest how far has the weight fallen fall Submitted Saturday June 19 at 7 22 PM m Submit

Q 40 A wooden disc of mass M and radius R has a single loop of wire wound on its circumference It is mounted on a massless rod of length d The ends of the rod are supported at its ends so that the rod is horizontal and disc is vertical A uniform magnetic field Bo exists in vertically upward direction When a current I is given to the wire one end of the rod leaves the support Find least value of I d 2 A d 2 O Bo B

Q 41 A uniform ring of mass M and radius R carries a current I see figure The ring is suspended using two identical strings OA and OB There exists a uniform horizontal magnetic field Bo parallel to the diameter AB of the rin Calculate tension in the two strings Given 0 60 A www 00 Bo B

Problem 4 8 Let the system of Problem 4 7 be set in motion with the initial conditions x A y 0 x y 0 at t 0 Show that the normal mode amplitudes are Xo m M A and Yo A to yield and X where M m m Express these displacements as and A M m cos wit m cos w t y A mi M cos wit cos w2t 2A x 2 A cos wmt cos wat m m sin wmt sin wat M y 2A sin wmt sin wat my M where wm w2w 2 and wa w W 2 122 579

1 A cubical block of mass m and side length b is placed on a smooth floor A smooth and rigid rod of length L and with negligible mass is leaning against the block A sphere of mass M is attached to the upper end of the rod The lower end of the rod is fixed at point O but the rod can rotate freely around the point within the vertical plane Initially the angle between the rod and the floor is a while the system is at rest After releasing Choose correct statement s B 0 1 1 0 338 A 9mil vns Jn 8 A Speed of the block when angle between rod and the floor is 3 is b MgL sina sin mb ML sin B B Speed of the block when angle between rod and the floor is is b one2 2MgL sin a sin mb2 ML sin B C Angular speed of the rod when angle between rod and the floor is is D Angular speed of the rod when angle between rod and the floor is is 2MgL sin a sin mb cosec 3 ML2 MgL sin a sin 3

A large wheel of radius R 1 25 m can rotate about its fixed horizontal axle There is large number of special traps on its periphery Small identical balls fall into a trap at the top with negligible velocity and leave the trap at the bottom Collisions of balls at the top are perfectly inelastic After some time the balls start falling into the traps the wheel acquires a steady angular velocity Find suitable approximate value of this steady angular velocity w Acceleration due to gravity is g 10 m s 1

On a horizontal smooth surface a disc is placed at rest Another disc of same mass is coming with impact parameter equa to its own radius First disc is of radius r What should be the radius of coming disc so that after collision first disc move at an angle 45 to the direction of motion of incoming disc A 2r B r 2 1 r 2 1 D r 2

165 A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure The ratio of inertia of the loop about x axis to that about y axis is 1 1 2 1 2r semicircle DE

A solid sphere of radius 5 cm is resting on a rough horizontal surface A force F is applied at a height 3 cm from centre of mass in horizontal direction as shown Frictional force acting on the sphere is 3 cm IT 1 In forward direction nt 2 In backward direction he of 3 Initially in backward direction and after some time in dinocti

A force F is applied at the top of a ring of mass M and radius R placed on a rough horizontal surface as shown in figure Friction is sufficient ta prevent slipping The frictional force acting on the ring is

solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6 m s It ollides on the free end of an ideal spring whose other end is fixed The maximum compression roduced in the spring will be Force constant of the spring 36 N m 14 m B 2 8 m C 1 4 m D 0 7 m

56 A uniform solid cylinder of mass m and radius R is set in rotation about its axis and lowered with the lateral surface on to the horizontal plane with initial centre of mass velocity vo If the coefficient of friction between the cylinder and the plane is u find a how long the cylinder will move with sliding friction b the total work done by the sliding friction force on the cylinder

A small stone of mass m is attached to a light string which passes through a hollow tube The tube is held by one hand and the free end of the string by the other hand The mass is set into revolution in a horizontal circle of radius r with a speed v The string is pulled down shortening the radius of the circular path to r2 Which of the following is not correct W Ek have usual meanings T is tension Question Type Single 1 W2 3 11 2722 Correct Type

wheel of moment of inertia 2 Kg m is rotating about an axis passing through centre and erpendicular to its plane at a speed 60 rad s Due to friction it comes to rest in 5 minutes The gular momentum of the wheel three minutes before it stops rotating is 24 Kg m s B 48 Kg m s C 72 Kg m s D 96 Kg m s

A un block of side L rests on a rough horizontal surface with cofficient of friction A horizontal force F is applied on the block as shown If the coefficient of friction is sufficiently high so that the block does not slip before toppling the shift in the normal reaction from the centre of the cube is 1 3 Fa 2Mg 2Fa a 27 4 Fa Mg Fa Ma

78 A disc of mass M and radius R is placed on a rough horizontal surface A light rod of length 2R is fixed to the disc at point A as shown in the figure and 3 force Mg is applied at the other end of the rod 2 Find the minimum value of coefficient of friction upto one decimal place between disc and horizontal surface so that disc starts to roll without slipping a 0 2 c 0 6 RIA R 2R b 0 4 d 0 8 32 Mg

3 16 23 Figure shows a hemisphere of radius 4R A solid ball of radius R is released from position A It rolls without slipping along the inner surface of the hemisphere Linear speed of its centre of mass when the ball is at position B is A g 3 30gR 7 40gR B 4R 2 24gR V5 4 6qR

19 A particle of mass 2 kg is moving on a straight line y 2x 4 with velocity 2 m s Then magnitude of angular momentum of the particle w r t origin is X1 16 Kgm 5 sec 8 Kgm2 2 32 Kgm 5 sec Kgm

4 57 Two identical cylinders each of mass m on which light threads are wound symmetrically are arranged as in Fig 4 14 Find the tension of each thread in the process of motion Neglect the friction in the axle of the upper cylinder Fig 4 14

30 N are applied on a wheel as shown in the figure What is the magnitude and direction of the net torque about the axle of the wheel if the inner and outer radii of the wheel are 20 cm and 40 cm respectively F3 30 F2 3 8 m N clockwise O 1 2 m N counterclockwise 2 4 m N counterclockwise O 1 8 m N clockwise F

74 A uniform solid cylinder of mass 5 kg and radius 0 1 m is resting on a horizontal platform parallel to the x y plane and is free to rotate about its axis along the y axis The platform is given a motion in the x direction given by x 0 2 cos 10t m If there is no slipping then maximum torque acting on the cylinder during its motion is a 0 2 N m c 5 0 N m b 2 0 N m d 10 0 N m

A disc is made to rotate about a horizontal fixed axis with the help of a body of mass 5kg attached to a string wound around the disc The radius of the disc is 10 cm The body falls vertically through 10m in 10s starting from rest The moment of inertia of the disc is g 10 m s 1 1 3 85 kgm 3 5 85 kam 18 10 1 Valmis GJ 2X4 85 kgm 4 2 45 kgm

73 A disc of radius R is rolling purely on a flat horizontal surface with constant angular velocity The angle between the velocity and acceleration vectors of point Pis P C a zero b 45 c 135 d tan 1 2 74 A uniform solid cylinder of mass 5 kg and radius

View In English In the following figure the velocities are in ground frame and the cylinder is performing pure rolling on the plank velocity of point A would be 3 4 2VC 2VC Vp 2VC Vp 2 VC Vp D Ve

2 1 Two spheres are moving as shown in figure They are given initial velocity is such that they are just able co touch each other during subsequent motion Then choose correct option s Answer A B C D Your Attempt O AGM to 28R Vo M R AGM TAR Max speed of A Max speed of B 8R Gorrect answer 3GM TR BGM 12 M R P Rate this question

A stone of mass m 1 0kg is suspended from the free end of a wire that is wrapped around the outer rim of a pulley similar to what is shown in the figure The moment of inertia of the pulley is 1 0kg m radius of the pulley is 1 0m and turns on frictionless bearings The stone was released from rest and it fell a distance h of 1 0 m What is the speed of the stone after it fell the distance of 1 0 m O None O 9 8 m s O 9 8 m s O 3 13 m s M

A square plate has a moment of inertia I about an axis lying in the plane passing through its cente and making an angle 8 with one of the sides Which graph represents the variation of I with 0 I I K I 1 1 3 0 0 2 4 2 0 0

30 What is the applied centrifugal field at a point equivalent to 5 cm from the centre of a rotation and an angular velocity of 3000 rads second O 45000 rad2 cm s 2 O 450000 rad2 cm s 2 O 4500000 rad2 cm s 2 O 45000000 rad2 cm s 2

A ring and a disc roll on the horizontal surface without slipping with same linear velocity If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the Hisc is A 3 J B 4 J C 5 J D 6 J

19 A metallic wire is folded to form a square loop of side a It carries a current i and is kept perpendicular to a uniform magnetic field If the shape of the loop is changed from square to a circle without changing the length of the wire and current the amount of work done in doing so is a i Ba 2 c i Ba 4 1 6 b i Ba 2 951 Ba 1 4 i

only one force which always acts towards a fixed point O lying on the circumference Find ratio of 2 d 0 dt at the moment when 0 45 C is centre of circle to de dt

A solid cylinder has mass M radius R and length e Its moment of inertia about an axis assing through its centre and perpendicular to its own axis is 2MR2 Me2 MR2 Me2 3MR Me A B C 3 12 3 12 4 12 D MR2 Me 4 12

A disc of radius R and thickness centre and perpendicular to its plane Disc is melted and recast into a solid sphere The momen of inertia of a sphere about its diameter is A 5 B R has moment of inertia I about an axis passing through in 6 6 C 32 D 64

A point object of mass m is slipping down on a smooth hemispherical body of mass M and radius R The point object is tied to a wall by an ideal string as shown At certain instant shown in figure speed of the hemisphere is v and its acceleration is a Then speed Vp and ap acceleration of the point object is Assume all the surfaces in contact are frictionless String m 30 Vp v sin 60 R a

A rod PQ of mass M and length L is hinged at end P The rod is kepts horizontal by a massless tring tied to point Q as shown in the figure When string is cut the initial angular acceleration of the rod is 3g B P log 2g C 2g R

A simplified gear system for mechanical watch is shown knowing that gear A starts from rest with an angular acceleration Aa 6 5t rad s 2 determine the angular velocity Wc at t 5s given Ra 10mm Rb 20mm and Rc 35mm A idler gear C O www

A thin wire of length L and uniform linear mass density p is bent into a circular loop with centre O as shown The moment of inertia of the loop about an axis XX is X 1 3 PL 87 5pL 167 90 2 4 3 PL 16 3pL 877

a 4 414 A particle tied to a string of negligible weight and length lis velocity having time period T If the string length is swung in a horizontal circular path with constant angular shortened by 1 2 while the particle is in motion the time period is EAMCET Med 2000 b 27 Cor 72 420 42

71 A block of mass M length L and height H is kept at rest on a rough inclined plane of inclination a with the horizontal as shown If u is the coefficient of friction between the block and the inclined plane then the block topples over if 1 tana L H 3 tanx L H a L M 2 tana L H 4 tana L 2H

A uniform rod of mass m and length L is kept L 4 on a horizontal table with length on the table as shown in figure As the string attached to the end B is cut the angular acceleration of the rod about point C will be BINIGEN

A cylinder of mass m and radius R starts falling under gravity at t 0 as shown in figure If mass of chord is negligible the tension in each string will be consider no slipping anywhere H mg 3 mg 6 mg 4 mg 9

A semicircular lamina of mass m has radius r and centre C Its moment of inertia about an axis through its centre of mass and perpendicular to its plane is DIGI m 1 4 8 B 2m 12 m D 12 25 m 16 mr 97