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Question

A sphere of mass m and radius r rolls on a horizontal plane without slipping with a speed u. Now it rolls up vertically, then maximum height it would be attain will be

A
3u24g
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B
5u22g
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C
7u210g
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D
u22g
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Solution

The correct option is C 7u210g
at no slipping condition for sphere,
u=ωr
ω=ur
From energy conservation principle,
Initial energy= Final energy
Linear kinetic energy+rotational energy=final potential energy
12mv2+12Iω2=mgh

12mu2+12×25mr2(ur)2=mgh

12mu2+15mu2=mgh

710mu2=mgh

h=7u210g


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