Question

A bomb of mass $9kg$ explodes into pieces of masses $3kg$ and $6kg$. The velocity of mass $3kg$ in $16m/s$. The kinetic energy of mass $6kg$ in joule is

Answer 1

Given, $m_1=3kg,m_2=6kg,v_1=16m/s,K.E=?$

According to law of conservation of momentum :

$(m_1\times v_1)+(m_2\times v_2)=(m_1+m_2)v$

$(3\times 16)+(6\times (-v_2\left)\right)=(3+6)\times 0(-v_2)$ ( because both are moving in opposite directions)

$48-(6\times v_2)=0\Rightarrow 48=6\times v_2\Rightarrow v_2=8m/s$

$K.E=\frac{1}{2}\times m_2\times v_2^2$

$=\frac{1}{2}\times 6\times 8^2=3\times 64=192J$