Question

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. $\frac{1}{2}m{v}^2\times \frac{m}{(m+M)}$

Answer 1

The correct option is D $\frac{1}{2}m{v}^2\times \frac{m}{(m+M)}$

Hint: “Perfectly inelastic collision”

Formula used:

$P_i=P_f$

Solution:

$mv=(m+M)V$
$k_f=\frac{1}{2}(m+M)V^2=\frac{1}{2}(m+M){\left(\frac{mv}{m+M}\right)}^2$
$\frac{1}{2}m{v}^2\times \frac{m}{(m+M)}$

Final Answer: (a).