An inclined plane makes an angle $30^{o}$ with the horizontal. A groove (OA) of length = 5 m cut in the plane makes an angle $30^{0}$ with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is (g: 10 $m / s^{2}$ )

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4 s

3 s

1 s

2 s

answer is B.

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Detailed Solution

Acceleration of cylinder down the plane is

$a = (g \sin 30^{0}) (\sin 30^{0}) = 10 (\frac{1}{2}) (\frac{1}{2}) = 2.5 m / s^{2}$

time taken: t = $\sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 \times 5}{2.5}} = 2 s$

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