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Question

A block slides down a smooth inclined plane to the ground when released at the top, in time tsec. Another block is dropped vertically from the same point in the absence of the inclined plane and reaches the ground in t/2sec. Then the angle of the inclination of the plane with the vertical is:

A
30o
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B
45o
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C
60o
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D
75o
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Solution

The correct option is A 30o
Let height be h and the slope be θ
l=hsinθ
Component of g along the inclined =gsinθ
l=12gsinθt2
hsinθ=12gsinθt2
t=2hg×1sinθ
For second block:
h=12gt2
t=2hg
t=t2
Therefore, on simplifying ,
2=1sinθ
sinθ=12
θ=π6
965657_1063819_ans_978e790b9729447f86832391da44f3c9.png

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