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Question

A body starts from rest and slides down the inclined surface of a smooth inclined plane having inclination θ with the horizontal. The time taken by the body to reach the bottom is


A
2hg
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B
2lg
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C
1sinθ2hg
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D
sinθ2hg
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Solution

The correct option is C 1sinθ2hg
Body will move along along the inclined plane. Net force (F) along the inclined plane is mgsinθ


Hence, acceleration of body along the inclined surface is,
a=Fm=mgsinθm
a=gsinθ ...(i)
When body reaches the bottom, its displacement (s) along the inclined surface is l.
sinθ=hl

Applying equation of motion along the inclined surface,
s=ut+12at2
Here, s=l,u=0 and a=gsinθ
l=0+12×gsinθ t2
t2=2lgsinθ
[l=hsinθ]
t2=2hgsin2θ
t=1sinθ2hg

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