Question

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms${}^{-1}$. The KE of the other mass is :

• A. 324 J
• B. 486 J
• C. 256 J
• D. 524 J

Answer 1

The correct option is B 486 J

Given : Mass of the bomb initially at rest $M=30kg$

For first fragment $m_1=18kg$ $v_1=6$ $m{s}^{-1}$

For second fragment $m_2=12kg$ Momentum $=p_2$

Applying conservation of linear momentum before and after the explosion :

$MV=m_1{v}_1+p_2$

$M\left(0\right)=18\times 6+p_2$ $(\because V=0)$

$⟹|p_2|=108$ $kg$ $m{s}^{-1}$

Thus kinetic energy of the second fragment $K.E_2=\frac{p_2^2}{2m_2}$

$K.E_2=\frac{{108}^2}{2\times 12}=486$ $J$