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A Solid sphere of mass M and radius R is released from rest at the top of a frictionless inclined plane of length 'd' and inclination ?. 

In case (a) it rolls down the plane without slipping and in case (b) it slides down the plane 

The ratio of the acceleration of the sphere in case (a) to that in case (b) is 

(A) 1 

(B) 2/3 

(C) 5/7 

(D) 7/9

1 Answer

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Best answer

Correct option: (C) 5/7

Explanation:

case an acceleration down plane without slipping

a1 = [(g sin θ) / {1 + (I / MR2)}]

= [(g sin θ) / {1 + {{(2/5)MR2} / MR2)}}]

= g sin θ(5/7)

case(b) slides down the plane

a2 = g sin θ

hence (a1 / a2) = (5/7)   

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