A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
$\frac{1}{2}m{v^2} \times \frac{m}{{(m + M)}}$
$\frac{1}{2}m{v^2} \times \frac{M}{{(m + M)}}$
$\frac{1}{2}m{v^2} \times \frac{{(M + m)}}{M}$
$\frac{1}{2}M{v^2} \times \frac{m}{{(m + M)}}$
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
By conservation of momentum,$mv + M \times 0 = (m + M)V$
Velocity of composite block $V = \left( {\frac{m}{{m + M}}} \right)\,v$
K.E. of composite block $ = \frac{1}{2}(M + m){V^2}$
$ = \frac{1}{2}(M + m)\,{\left( {\frac{m}{{M + m}}} \right)^2}{v^2} = \frac{1}{2}m{v^2}\left( {\frac{m}{{m + M}}} \right)$