Question

A shell at rest on a smooth horizontal surface explodes into two fragments of masses $m_1$ and $m_2$. If just after explosion $m_1$ move with speed $u$, then work done by internal forces during explosion is

• A. $\frac{1}{2}(m_1+m_2)\frac{m_2}{m_1}{u}^2$
• B. $\frac{1}{2}(m_2+m_1)u^2$
• C. $\frac{1}{2}{m}_1{u}^2(1+\frac{m_1}{m_2})$
• D. $\frac{1}{2}(m_2-m_1)u^2$

Answer 1

The correct option is C $\frac{1}{2}{m}_1{u}^2(1+\frac{m_1}{m_2})$

Using momentum conservation, $m_{1}u=m_{2}v$
Now using work energy theorem,
$W=\frac{m_1{u}^2}{2}+\frac{m_2{v}^2}{2}$
$W=\frac{m_1{u}^2}{2}\left(\frac{m_1+m_2}{m_2}\right)$