Question

A mass $m$ moves with a velocity $v$ and collides inelastically with another identical mass at rest. After collision, the first mass moves with velocity $\frac{v}{\sqrt{3}}$ in a direction perpendicular to the initial direction of motion. The speed of the $2^{\text{nd }}$ mass after collision is

• A. $\frac{2v}{\sqrt{3}}$
• B. $\frac{v}{\sqrt{3}}$
• C. $v$
• D. $\sqrt{3}v$

Answer 1

Answer: (A)

In $x$ -direction $mv+0=0+m{v}_1\cos \theta \dots$ (i)
where $v_1$ is the velocity of $2^{\text{nd }}$ mass. In $y$ -direction
$0=\frac{mv}{\sqrt{3}}-m{v}_1\sin \theta$
or $m{v}_1\sin \theta =\frac{mv}{\sqrt{3}}\dots$(ii)
Squaring and adding eqns. (i) and (ii), we get
$v_1^2=v^2+\frac{v^2}{3}=\frac{4v^2}{3}$
$\therefore v_1=\frac{2v}{\sqrt{3}}$