Question

Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is $\sqrt{\frac{n L}{2 \sqrt{3} g}}$ . Find $n$ .

Answer 1

$-mv \, cos \, 60^{o} \, + \, 2mu=0 \, \Rightarrow \, v=4u$
$\frac{1}{2}m \, \left[\right.v^{2} \, +u^{2} \, +2uv \, cos \, 120^\circ \left]\right.+\frac{1}{2}mu^{2} \, =mgx \, \, sin60^\circ $
$\Rightarrow v^{2}=\frac{8}{7}\sqrt{3} \, \, gx \, \, \, \Rightarrow \, \, \, a_{r} \, \, = \, \, \frac{4 \sqrt{3}}{7}g$
$\therefore \, \, t=\sqrt{\frac{2 L \, \, \times \, \, 7}{4 \sqrt{3} \, g}}$