Question

A stationary shell explodes into two fragments having masses in the ratio of $1:2.$ The heavier fragment attains a kinetic energy of $100J$. The kinetic energy released in the explosion is

• A. $200J$
• B. $150J$
• C. $300J$
• D. $600J$

Answer 1

Answer: (C)

$300J$

Let mass of pieces are $m_1=m$ and $m_2=2m$

Applying conservation of momentum,

$m_1{v}_1=m_2{v}_2$

$⟹m{v}_1=2m{v}_2$

$⟹v_1=2v_2$

Now,

$⟹\frac{1}{2}{m}_2{v}_2^2=100$

$⟹\frac{1}{2}\times 2m\times \left({\frac{v_1}{2}}^2\right)=100$

$⟹\frac{1}{2}{m}_1{v}_1^2=100\times \frac{1}{2}\times 4=200J$

So, Total Kinetic Energy $=300J$