Question

A wooden block of mass $1950$ g is at rest on a smooth horizontal table. A bullet of mass $50$ g is fired into the block and gets embedded in it. The velocity with which the bullet strikes the block is ${100ms}^{-1}$; find their common velocity.

• A. ${3.5ms}^{-1}$
• B. ${0.625ms}^{-1}$
• C. ${1.25ms}^{-1}$
• D. ${2.5ms}^{-1}$

Answer 1

The correct option is D ${2.5ms}^{-1}$

Let the common velocity be $V$.

Applying conservation of linear momentum : $P_f=P_i$

Or $(m_{block}+m_{bullet})V=m_{block}{u}_{block}+m_{bullet}{u}_{bullet}$

Or $(1950+50)V=1950\times 0+50\times 100$

$⟹V=2.5m/s$