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Question

A small object of uniform density rolls up a curved surface with an initial velocity v (see the figure). It reaches upto a maximum height h=3v24g, with respect to the initial position. The object is a:


A
ring
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B
solid sphere
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C
hollow sphere
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D
disc
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Solution

The correct option is D disc
Applying mechanical energy conservation, since work done by friction Wf=0 in pure rolling,
Loss in KETrans+Loss in KERot=Gain in PE
or 12mv2+12Iω2=mgh
[v=Rω for pure rolling]
12mv2+12I(v2R2)=mgh
12mv2+12I(v2R2)=mg(3v24g)
12I(v2R2)=3mv24mv22
I=mv24×2R2v2
I=mR22
Hence the object is a disc.

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