A sphere is given an initial angular velocity ω0 and kept on a long rough inclined plane of inclination θ and coefficient of friction μ. Match Column-I with Column-II. Column-I Column-II (A) θ=37°, μ=

Question

A sphere is given an initial angular velocity ω0 and kept on a long rough inclined plane of inclination θ and coefficient of friction μ. Match Column-I with Column-II.

Column-I	Column-II
(A) θ=37°, μ=1, ω0 clockwise	(P) Acceleration just after t=0 is zero
(B) θ=45°, μ=1, ω0 anticlockwise	(Q) Acceleration just after t=0 is upwards
(C) θ=53°, μ=1/3, ω0 clockwise	(R) Starts pure rolling while ascending
(D) θ=30°, μ=1/2, ω0 anticlockwise	(S) Starts pure rolling while descending
	(T) Never rolls purely

TestHub · Accepted Answer

Compare downhill gravity with limiting friction for the initial direction of slip.

Track translational and angular speeds until the rolling condition is first reached. This gives A-P,R; B-Q,R; C-S; D-T.

Physics - Rotation Question with Solution | TestHub

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