Question

A bullet of mass $m$ moving vertically upwards instantaneously with a velocity '$u$' hits the hanging block of mass '$m$' and gets embedded in it, as shown in the figure.The height through which the block rises after the collision. (assume sufficient space above block) is:

• A. $u^2/2g$
• B. $u^2/16g$
• C. $u^2/8g$
• D. $u^2/4g$

Answer 1

The correct option is C $u^2/8g$

Momentum is conserved.
i.e.
$mu=mv+mv$

$v=\frac{u}{2}$

The kinetic energy is completely converted to potential when it climbs.

$\frac{1}{2}2m{v}^2=2mgh$

$h=\frac{1}{2g}{v}^2$

$h=\frac{1}{8g}{u}^2$