Question

A ball impings directly upon another ball at rest and is itself brought to rest by the impact. If half of initial kinetic energy is destroyed in the collision, the coefficient of restitution is?

• A. $0.3$
• B. $0.4$
• C. $0.5$
• D. $0.6$

Answer 1

The correct option is C $0.5$

Let m be the mass and v be the velocity of first ball, M is the mass and V is the velocity of the second ball

Then

$mv=MV$

and $V=ev$

Since energy lost $=$ half the initial energy

$\frac{1}{2}m{v}^2=\frac{1}{2}M{V}^2=\frac{1}{2}\left(\frac{1}{2}m{v}^2\right)$

Putting $V=ev$

$\frac{1}{2}m{v}^2+\frac{1}{2}mv.ev=\frac{1}{4}m{v}^2$

or $\frac{1}{4}m{v}^2=\frac{1}{2}mv.ev$

$e=\frac{1}{2}$

Co efficient of restitution is $0.5$