A bullet of mass $\mathrm{m}$ moving with velocity 'v' is fired into a wooden block of mass 'M'. If the…
A bullet of mass $\mathrm{m}$ moving with velocity 'v' is fired into a wooden block of mass 'M'. If the bullet remains embedded in the block, the final velocity of the system is
$\frac{v}{m(M+m)}$
$\frac{m+M}{m}$
$\frac{\mathrm{M}+\mathrm{m}}{\mathrm{mv}}$
$\frac{\mathrm{mv}}{\mathrm{m}+\mathrm{M}}$
Solution
Since there is no extra force other than the action and reaction force so the linear momentum should be conserved.
Suppose the system moves with velocity V then momentum before collision is mv and that after collision will be $(M+$ $\mathrm{m}) \mathrm{V}$
Equating both we get $m v=(M+m) V$ or $V=\frac{m}{m+M}^{v}$