Question

Find the displacement of the wedge when the mass 'm' has comes out of the wedge. There is no friction anywhere.

• A. $\frac{ml}{M+2m}$
• B. $\frac{ml}{M+m}$
• C. $\frac{ml-mlcos\theta }{M+2m}$
• D. $\frac{ml+mlcos\theta }{M+2m}$

Answer 1

The correct option is C $\frac{ml-mlcos\theta }{M+2m}$

Let wedge move towards right by distance x; then
$\Delta x_{CM}=\frac{m(lcos\theta +x)+Mx+m(x-l)}{m+M+m}$
$0=mlcos\theta -ml+(m+M+m)x$
$x=\frac{ml-mlcos\theta }{2m+M}$