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
1sinθ√2hg
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D
sinθ√2hg
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Solution
The correct option is C1sinθ√2hg 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×gsinθt2 ⇒t2=2lgsinθ [∵l=hsinθ] ⇒t2=2hgsin2θ ∴t=1sinθ√2hg