Question

A bomb of mass 9 kg explodes into two pieces of mass 3 kg and 6 kg. The velocity of mass 3 kg is 16ms${}^{-1}$. The kinetic energy of mass 6 kg in joule is :

• A. 768
• B. 96
• C. 384
• D. 192

Answer 1

The correct option is D 192

Let,
$v_1$ and $v_2$ be the velocities of the two masses, $m_1$ and $m_2$ be the masses of the two masses,
According to law of conservation of momentum
$m_1{v}_1=m_2{v}_2$
$v_2=\frac{m_1{v}_1}{m_2}$
$v_2=\frac{3\times 16}{6}=8m{s}^{-1}$
Hence, kinetic energy is
$E=\frac{1}{2}{m}_2(v_2{)}^2$
$E=\frac{1}{2}6(8{)}^2$
$E=\frac{1}{2}6\left(64\right)=192J$