Question

Find the height by which the sphere rises when the wedge moves and touches the wall. The distance between the wedge and the wall is $10\text{m}$ and the wedge is moved to the left until it touches the wall. Answer in metre.
Take $\sqrt{3}=1.73$

Answer 1

By condition of wedge constrained the displacement, velocity and acceleration along normal to the common interface is same.

Let $S_w$ be the displacement of the wedge,
And $S_s$ be the displacement of the sphere.
$S_w\sin \theta =S_s\cos \theta$
$\Rightarrow S_s=S_w\tan \theta$
$\Rightarrow S_s=10\tan {30}^{\circ }$
$S_s=\frac{10}{\sqrt{3}}\text{m}$