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5.Work, Energy, Power and Collision
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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
$\frac{1}{2}m{v^2} \times \frac{m}{{(m + M)}}$
B
$\frac{1}{2}m{v^2} \times \frac{M}{{(m + M)}}$
C
$\frac{1}{2}m{v^2} \times \frac{M+m}{{(M)}}$
D
$\frac{1}{2}m{v^2} \times \frac{2m}{{( M+m)}}$
Solution
Initial momentum of system, $p_{1}=m v$
Let $V$ be the velocity of composite system
Final momentum os system, $p_{2}=(m+M) V$
By conservation of momentum, $m v=(m+M) V$
$\therefore V=\frac{m v}{m+M}$
Kinetic energy of composite block, $K=\frac{1}{2}(M+m) V^{2}=\frac{1}{2}(M+m)\left(\frac{m v}{m+M}\right)^{2}=\frac{1}{2} m v^{2} \times \frac{m}{m+M}$
Standard 11
Physics
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