c
The force acting on the satellite is given by

\(F =\frac{ d }{ d t }( M v )\)

\(F=\frac{ dv }{ dt } M + v \frac{ dM }{ dt }\)

\(F= M \frac{ dv }{ dt }+ v (\alpha v )\)

We know that the net force is zero. \(F =0\),

\(M \frac{ d v }{ dt }=- v (\alpha v )\)

\(\frac{d v}{d t}=a=-\frac{\alpha v^{2}}{M}\)