Question

Two balls, each of mass $m$, moving in the same direction with speeds $v$ and $3v$, collide with each other. If the collision is perfectly inelastic, find out the loss in kinetic energy.

• A. $\frac{1}{2}m{v}^2$
• B. $2m{v}^2$
• C. $\frac{3}{2}m{v}^2$
• D. $m{v}^2$

Answer 1

The correct option is D $m{v}^2$

After colliding, both balls will move with same velocity, say $v_0$
Applying conservation of momentum,
$m_1{v}_1+m_2{v}_2=(m_1+m_2)v_0$
$mv+3mv=(m+m)v_0$
$4mv=2m{v}_0$
$\Rightarrow v_0=2v$

Initial kinetic energy $(KE{)}_i=\frac{1}{2}m{v}^2+\frac{1}{2}m(3v{)}^2$
$=5m{v}^2$
Final kinetic energy = $(KE{)}_f=\frac{1}{2}2m(2v{)}^2=4m{v}^2$
Change in kinetic energy = $\Delta k=k_j-k_i$
$\Delta k=5m{v}^2-4m{v}^2$
$\Delta k=m{v}^2$

Hence, $\left(D\right)$ is the correct answer.