[UPSC IFoS 2011] Special Theory of Relativity (Q374, 10M)

A particle of rest mass 'M' moving at a velocity 'u' collides with a stationary particle of rest mass 'm'. If the particles stick together, show that the speed of the composite ball is equal to v = \frac{u \gamma M}{(\gamma M + m)}, \quad \text{where } \gamma = \frac{1}{\sqrt{1 - \frac{u^2}{c^2}}}