Question

In the figure shown, an inclined plane makes an angle $30^{\circ }$ with the horizontal. $A$ groove $OA=5m$ cut in the plane makes an angle $30^{\circ }$ with $OX.A$ short smooth cylinder is free to slide down in the groove due to the influence of gravity. The time (in s) taken by the cylinder to reach from $A$ to $O$, if released from rest from $A$, is $\left(g=10m/s^2\right)$

Answer 1

Answer: 2

$a=g{\sin }^2\theta$
$a=10\times {\sin }^{2}30^{\circ }$
$=10\times \frac{1}{4}=\frac{5}{2}m/s^2$
$S=\frac{1}{2}a{t}^2$
$t=\sqrt{\frac{2S}{a}}$
$\Rightarrow t=\sqrt{\frac{2\times 5}{5/2}}$
$=\sqrt{4}=2s$