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 $288\text{J}$

Let the velocity and mass of $4\text{kg}$ piece by $v_1$ and
velocity and mass of $12\text{kg}$ piece be $v_2$ and $m_2$
Applying conservation of linear momentum
$m_2{v}_1=m_1{v}_2$
$\Rightarrow v_1=\frac{12\times 4}{4}=12{\text{ms}}^{-1}$
Kinetic energy is
$\therefore K{E}_1=\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}\times 4\times 144=288J$
The correct option is (B)