Q.

A body of mass m slides down a smooth incline and reaches the bottom with a velocity v. Now smooth incline surface is made rough and the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been

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a

2v

b

v

c

25v

d

v/2

answer is D.

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Detailed Solution

For a sliding body of mass m,  vbody =2gh=vFor a rolling ring of same mass m,vring =2ghβ=2gh1+ImR2=2gh1+mR2mR2=2gh2=gh=v2
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A body of mass m slides down a smooth incline and reaches the bottom with a velocity v. Now smooth incline surface is made rough and the same mass was in the form of a ring which rolls down this incline, the velocity of the ring at the bottom would have been