A satellite in a force free space sweeps stationary interplanetary dust at a rate (dM/dt) = αv. The acceleration of satellite is

A satellite in a force free space sweeps stationary interplanetary dust at a rate (dM/dt) = αv. The acceleration of satellite is

\[a.\frac{-2 \alpha v^2}{M}\] \[b.\frac{- \alpha v^2}{M}\] \[c.\frac{- \alpha v^2}{2M}\] \[d.- \alpha v^2\] 

 [1994]

Always remember that F=ma is a special case only when the mass is a constant. There are some cases such as rocket, satellite gathering space dust in which mass is not a constant and will keep changing w.r.t time. For rocket the mass will decrease as the fuel is spent (more than 80% of rocket mass is fuel Hydrogen and Oxygen. For the satellite gathering mass, the mass will increase.

\[ F = ma \quad \text{(Special case)} \] \[F=\text{rate of change of momentum} \text{(General case)}\]\[ F = \frac{d(mv)}{dt} \] \[ F = m \frac{dv}{dt} + v \frac{dm}{dt} \] \[ 0 = m a + v \cdot \alpha v \] \[ a = -\frac{\alpha v^2}{m} \]