A stationary body explodes into two fragments of masses `m_(1)` and `m_(2)`. If momentum of one fragment is `p`, the energy of explosion is

Options

A. `(p^(2))/(2(m_(1)+m_(2)))`
B. `(p^(2))/(2sqrt(m_(1)m_(2)))`
C. `(p^(2)(m_(1)+m_(2)))/(2m_(1)m_(2))`
D. `(p^(2))/(2(m_(1)-m_(2)))`

Answer

C

Explanation

`u_(1)=p/m_(1),u_(2)=p/m_(2)`
`E=1/2m_(1)u_(1)^(2)+1/2m_(2)u_(0)^(2)`
`=1/2[m_(1)(p^(2))/(m_(1)^(2))+m_(2)(p^(2))/(m_(2)^(2))]=(p^(2)(m_(1)+m_(2)))/(2m_1m_2)`