A double stage rocket has an initial mass `M_(1)`. Gas is exhausted from the rocket at a constant rate of dm/dt and with an exhaust velocity u relative to the rocket. When the mass of the rocket reaches the value `'mu'` the first state of mass m is disengaged from the rocket then the rocket continues the second stage at the same rate (dm/dt) and exhaust velocity (u) as in the first stage unit it reaches a mass `M_(f)`. If gravity is neglected and the rocket has started from rest, the velocity of the rocket at the end of first stage is

Options

A. `u lin ((m_(i))/(mu))`
B. `u ln((M_(i) - mu)/(M_(i)))`
C. `u ln((M_(i) + mu)/(M_(i)))`
D. `u ln((mu)/(M_(i)))`

Answer

A