Question

A ball of mass $m$ moving horizontally with velocity $V_0$ strikes a block of same mass which is suspended by a light inextensible string of length $l$. After inelastic collision ,combined block rise upto position where string makes an angle of ${60}^{\circ }$ with vertical. Find $V_0$.

• A. $\sqrt{\frac{g}{l}}$
• B. $\sqrt{l{g}^2}$
• C. $\sqrt{4gl}$
• D. $\sqrt{2gl}$

Answer 1

The correct option is C $\sqrt{4gl}$

By conservation of momentum before and just after the collision,
$m{V}_0=2m\left(V\right)$
$V=\frac{V_0}{2}$
By conservation of energy,
$\frac{1}{2}2m{\left(\frac{V_0}{2}\right)}^2=2mgh=2mgl(1-\cos {60}^{\circ })$
$\frac{\text{/}m{V}_0^2}{4}=\text{/}mgl\Rightarrow V_0=\sqrt{4gl}$