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A wooden block sliding down from the top of a smooth inclined plane starting from rest takes $t_{1}$ , seconds to reach the bottom of the plane and attains velocity V₁. Another block of twice the mass falling freely from the same height takes $t_{2}$ sec. to reach the bottom of the plane and attains V₂. If angle of inclination of the plane is 30º

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$v_{1} = v_{2} & t_{2} = 2 t_{1}$

$v_{1} > v_{2} & t_{1} > t_{2}$

$v_{1} = v_{2} & t_{1} = t_{2}$

$v_{1} = v_{2} & t_{1} = 2 t_{2}$

answer is B.

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Detailed Solution

The velocity attained will be same since the heights are same. But the acceleration for the vertical fall is g, and for the sliding wooden block it will be $gsin 30 ° = 0.5 g$

So, $v_{1} = v_{2} and t_{1} = 2 t_{2}$

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