A body of mass M at rest is struck by a moving body of mass. Prove that the fraction of the initial kinetic energy of mass transferred to the struck body is `(4Mm)/((m+M)^(2))`

Explanation

To solve the problem, we need to analyze the collision between two bodies: a mass \( M \) at rest and a mass \( m \) moving with an initial velocity \( u \). We will derive the fraction of the initial kinetic energy of mass \( m \) that is transferred to mass \( M \).

### Step-by-Step Solution:

1. **Initial Kinetic Energy of Mass \( m \)**:
The initial kinetic energy \( E_1 \) of the moving mass \( m \) is given by:
\[
E_1 = \frac{1}{2} m u^2
...