Question

A rod of mass 2m moves vertically downward on the surface of wedge of mass m as shown in figure. Find the relation between velocity of rod, u and that of the wedge, v at any instant.

• A. $\frac{u}{v}=tan\theta$
• B. $\frac{u}{v}=sin\theta$
• C. $\frac{v}{u}=tan\theta$
• D. $\frac{u}{v}=cos\theta$

Answer 1

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

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