Question

A bomb of mass 9 kg explodes into two pieces of masses 3 kg and 6 kg. The velocity of mass 3 kg is $16m{s}^{-1}$. The kinetic energy of mass 6 kg is

• A. 96 J
• B. 384 J
• C. 192 J
• D. 768 J

Answer 1

The correct option is C 192 J

Substitute momentum without calculating the velocity since both velocity and mass are variables in the expression for kinetic energy. It is better use kinetic energy in terms of momentum and mass.
Since $p_{ini}=0=p_{fin}$;
Since momentum is conserved, $p_1=p_2$;
$3v_1=6v_2$;

${KE}_2=\frac{{p_2}^2}{2m_2}=\frac{{p_1}^2}{2m_2}$;

$p_1=3\ast 16=48$;

$\frac{{p_1}^2}{2m_2}={48}^2/2\ast 6=192J$;