Question

A body of mass 5 kg moving with a speed of $3m{s}^{-1}$ collides head on with a body of mass 3 kg moving in the opposite direction at a speed of $2m{s}^{-1}$. The first body stops after the collision. The total K.E. produced in the collision is

• A. -15 J
• B. -13.5 J
• C. 12.4 J
• D. - 16.2 J

Answer 1

Answer: (A)

-15 J

Let the velocity of the second body be $v$ after collision.

Applying conservation of momentum: $m_1{u}_1-m_2{u}_2=0+m_{2}v$

$\therefore$ $5\times 3-3\times 2=3v$ $⟹v=3$ $m{s}^{-1}$

Loss in kinetic energy $\Delta K.E=\frac{1}{2}{m}_2{v}^2-(\frac{1}{2}{m}_1{u}_1^2+\frac{1}{2}{m}_2{u}_2^2)$

$\therefore$ $\Delta K.E=\frac{1}{2}3(3{)}^2-\frac{1}{2}5(3{)}^2-\frac{1}{2}3(2{)}^2=-15J$