Question

A ball A moving with a certain velocity collides, with another ball B of the same mass at rest. If the coefficient of restitution is e. the ratio of the velocity of A and B just after the collision is:

• A. $\frac{1+e}{1-e}$
• B. $\frac{1+e}{2}$
• C. $\frac{1-e}{2}$
• D. $\frac{1-e}{1+e}$

Answer 1

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

Both balls have same mass $m$

the linear momentum before collision is $mu+0=mu$

suppose after collision they have velocities $V_1$ and $V_2$

then the momentum after collision will be $m{V}_1+m{V}_2=m(V_1+V_2)$

momentum should be conserved so $mu=m(V_1+V_2)$ or $V_1+V_2=u$.......(1)

coefficient of restitution is defined as $e=\frac{Separation}{Approach}=\frac{V_2-V_1}{u-0}$ so we get $V_2-V_1=eu$...........(2)

solving equation-1 and equation-2 we get $\frac{V_1}{V_2}=\frac{1-e}{1+e}$