A sphere of radius ‘a’ and mass ‘m’ rolls along a horizontal plane with constant speed ν0. It encounters an inclined plane at angle θ and climbs upward. Assuming that it rolls without slipping, how far up, the sphere will travel ?
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a
25ν02gsinθ
b
ν022gsinθ
c
7ν0210gsinθ
d
ν025gsinθ
answer is C.
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Detailed Solution
Conservation of Energy, Ui+Ki=Uf+Kf⇒0+12mv02+12Iω02=mgh+0⇒12mv02+1225ma2v0a2=mgh⇒h=710v02g Now, length along the plane =L=hsinθ=7v0210gsinθ