Question

A ball of mass m moving horizontally at a speed v collides with the bob of a simple pendulum at rest. The mass of the bob is also m. If the collision is perfectly inelastic, the height to which the two balls rise after the collision will be given by

• A. $\frac{v^2}{g}$
• B. $\frac{v^2}{2g}$
• C. $\frac{v^2}{4g}$
• D. $\frac{v^2}{8g}$

Answer 1

The correct option is D

$\frac{v^2}{8g}$

In an inelastic collision, the two bodies stick together. After the collision, the speed of the ball and the bob (sticking together) is $v^{\prime }=\frac{v}{2}$.
The height to which they will rise is given by $v^{\prime }=\sqrt{2g{h}^{\prime }}$
$\Rightarrow h^{\prime }=\frac{v^{\prime 2}}{2g}=\frac{v^2}{8g}$.
Hence, the correct choice is (d).