A satellite of mass m is launched vertically upwards with an initial speed `sqrt((GM)/®)` from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass `m/10` in a direction opposite to the initial direction of the satellite, so that subsequently the satellite escapes to infinity. The minimum kinetic energy of the rocket at ejection needed is (G is the gravitational constant, M is the mass of the earth):

Options

A. `m/20 (u^2+113/200(GM)/R)`
B. `5m (u^2-119/200(GM)/R)`
C. `(3m)/20 (u+sqrt((5GM)/(6R)))^2`
D. `(m)/20 (u-sqrt((2GM)/(3R)))^2`

Answer

B