Question

A rod of mass $2\text{m}$ moves vertically downward on the surface of wedge of mass as shown in the figure. Find the relation between velocity of rod and that of the wedge at any instant.

• A. $u=v\tan \theta$
• B. $u=v\tan 2\theta$
• C. $v=u\tan \theta$
• D. $v=u\sin \theta$

Answer 1

The correct option is A $u=v\tan \theta$

Using wedge constraint.
Component of velocity of rod along perpendicular to inclined surface is equal to velocity of wedge along that direction.
$u\cos \theta =v\sin \theta$
$\frac{u}{v}=\tan \theta$
$u=v\tan \theta$