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Question

A solid sphere of radius a and mass m rolls along the horizontal plane with constant speed vo. It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up the iclined plane, sphere will travel (along the incline)?

A
25v2ogsinθ
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B
107v2ogsinθ
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C
15v2ogsinθ
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D
710v2ogsinθ
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Solution

The correct option is D 710v2ogsinθ

From energy conservation,
mgh=12mv2o+12Iω2
mgh=12mv2o+12×25ma2×v2oa2
gh=12v2o+15v2o
gh=710v2o
h=710v2og
From triangle, sinθ=hl
Then, h=lsinθ=710v2og
l=710v2ogsinθ

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