A satellite in force-free space sweeps stationary interplanetary dust at a rate $dM/dt=\alpha v$ where M is the mass, v is the velocity of the satellite and $\alpha$ is a constant. What is the deacceleration of the satellite

(1) $-2\alpha {v}^{2}/M$

(2) $-\alpha {v}^{2}/M$

(3) $+\alpha {v}^{2}/M$

(4) $-\alpha {v}^{2}$

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Variable mass system

(3) $F=\frac{dp}{dt}=v\text{\hspace{0.17em}}\left(\frac{dM}{dt}\right)=\alpha \text{\hspace{0.17em}}{v}^{2}$

$a=\frac{F}{M}=\frac{\alpha \text{\hspace{0.17em}}{v}^{2}}{M}$

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