Question

A bomb of mass $16\text{kg}$ at rest explodes into two pieces of masses $4\text{kg}$ and $12\text{kg}$. The velocity of the $12\text{kg}$ mass is $4{\text{ms}}^{-1}$. The kinetic energy of the other mass is

• A. $144\text{J}$
• B. $288\text{J}$
• C. $192\text{J}$
• D. $96\text{J}$

Answer 1

The correct option is B $288\text{J}$

Here, momentum of the system is remaining conserved as no external force is acting on the bomb (system).

Initial momentum (before explosion )
= Final momentum (after explosion)
Let velocity of $4\text{kg}$ mass be $v{\text{ms}}^{-1}$. From momentum conservation, we can say that its direction is opposite to velocity of $12\text{kg}$ mass.
From $p_i=p_f\Rightarrow 0=12\times 4-4\times v$
or $v=12\text{m/s}$
$\therefore \text{KE of}4\text{kg mass}=\frac{4\times (12{)}^2}{2}=288\text{J}$