A rigid cylinder is kept on a smooth horizontal surface as shown. If List-I indicates velocities of various points (3 - centre of cylinder, 2 - top point, 4 - bottom point, 1 - on the level of 3 at th

Question

A rigid cylinder is kept on a smooth horizontal surface as shown. If List-I indicates velocities of various points (3 - centre of cylinder, 2 - top point, 4 - bottom point, 1 - on the level of 3 at the rim) on it, choose correct state of motion from List-II.

List - I	List - II
(I) $v_{1} = \hat{i} + \hat{j}, v_{2} = 2 \hat{i}$	(P) Pure rotation about centre
(II) $v_{1} = \hat{i} + \hat{j}, v_{3} = - \hat{i}$	(Q) Rolling without slipping to left
(III) $v_{2} = \hat{i}, v_{3} = 0$	(R) Rolling without slipping to right
(IV) $v_{4} = 0, v_{1} = - \hat{i} - \hat{j}$	(S) Not possible
	(T) Rolling with slipping to right

TestHub · Accepted Answer

Let centre velocity be v x ​ along x and angular velocity be ω along z. v 1 ​ = ( v x ​ , − ω R ) , v 2 ​ = ( v x ​ − ω R , 0 ) , v 4 ​ = ( v x ​ + ω R , 0 ) Case I gives v x ​ = 1 and ω R = − 1 , so the bottom is at rest: R. Case II gives contradictory horizontal velocities: S. Case III has a stationary centre: P. Case IV gives v x ​ = − 1 and ω R = 1 : Q. I → R , II → S , III → P , IV → Q

Physics - Rotation Question with Solution | TestHub

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