Question

A bomb of $12kg$ mass explodes into two pieces of masses $4kg$ and $8kg$. The velocity of $8kg$ mass is $6m{s}^{-1}$. The kinetic energy of the other mass is

• A. $48J$
• B. $32J$
• C. $24J$
• D. $288J$

Answer 1

The correct option is D

$288J$

Step 1: Given data and assumption

The mass of both the pieces of the bomb are ${\mathrm{m}}_1=4kg$and ${\mathrm{m}}_2=8kg$ respectively.

The velocity of ${\mathrm{m}}_2$ is $6m{s}^{-1}$.

Let the velocity of ${\mathrm{m}}_1$ be $vm{s}^{-1}$.

Step 2: Calculating kinetic energy

According to the law of conservation of momentum, the total momentum of a system remains constant.

Since, the momentums will be equal, the velocity of the mass ${\mathrm{m}}_1$ can be calculated as shown below:

$$\begin{gathered} 4kg\times vm{s}^{-1}=8kg\times 6m{s}^{-1} \\ v=\frac{8\times 6}{4}=12m{s}^{-1} \end{gathered}$$

The kinetic energy of the other mass is calculated as,

$$\begin{gathered} \frac{1}{2}\mathrm{m}{v}^2 \\ =\frac{1}{2}\times 4kg\times {12}^{2}m{s}^{-1} \\ =288J \end{gathered}$$

The kinetic energy of the other mass is $288J$

hence, option (d) is correct