A ball of mass m is moving with a velocity v and it suffers head - on collision with another identical ball at rest . What should be the coefficient of restitution if one - fourth of initial kinetic energy is lost in collision ?

Explanation

To solve the problem step by step, we will analyze the situation involving the two identical balls during the collision and apply the principles of conservation of momentum and kinetic energy.

### Step 1: Initial Kinetic Energy
The initial kinetic energy (KE_initial) of the moving ball can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 \]
where \(m\) is the mass of the ball and \(v\) is its velocity.
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