Question

A bomb of mass $9kg$ explodes into the fragments of masses $3kg$ and $6kg$. The velocity of mass $3kg$ is $16{ms}^{-1}$. The energy of explosion is equal to:

• A. $384J$
• B. $576J$
• C. $192J$
• D. $1152J$

Answer 1

The correct option is B $576J$

Mass of first fragment $m_1=3kg$

Velocity of the first fragment $v_1=16$ $m{s}^{-1}$

$\therefore$ Momentum of first fragment $P_1=m_1{v}_1=3\times 16=48$ $kg$ $m{s}^{-1}$

As the initial momentum of the bomb is zero, thus final momentum of the system must also be zero.

$⟹$ Momentum of the second fragment $P_2=P_1=48$ $kg$ $m{s}^{-1}$

Mass of second fragment $m_2=6kg$

Total energy of explosion $E=\frac{P_1^2}{2m_1}+\frac{P_2^2}{2m_2}$

$\therefore$ $E=\frac{{48}^2}{2\times 3}+\frac{{48}^2}{2\times 6}=576J$