Question

A sphere of mass $m$ moving with a constant velocity $u$ hits another stationary sphere of same mass. If $e$ is the coefficient of restitution, then ratio of velocities of the two spheres $\frac{v_1}{v_2}$ after collision will be

• A. $\frac{1-e}{1+e}$
• B. $\frac{1+e}{1-e}$
• C. $\frac{e+1}{e-1}$
• D. $\frac{e-1}{e+1}$

Answer 1

The correct option is B $\frac{1+e}{1-e}$

Step 1, Given data

Mass of the sphere = m

Initial velocity = u

Mass of the other sphere = m

Step 2,

From conservation of linear momentum:

$mu=m{v}_1+m{v}_2$
or $u=v_1+v_2...\left(i\right)$
From definition of $e$ :
$v_1-v_2=eu...\left(ii\right)$
Solving these two equations, we get
$v_1=\left(\frac{1+e}{2}\right)u$
and $v_2=\left(\frac{1-e}{2}\right)u$
$\therefore \frac{v_1}{v_2}=\left(\frac{1+e}{1-e}\right)$

Hence the ratio of velocity is as given above.