Question

A satellite in a force free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt}=\alpha v$, where M is the mass and v is the velocity of the satellite and $\alpha$ is a constant. The acceleration of the satellite is

• A. $-\frac{2\alpha v}{M}$
• B. $-\frac{\alpha v^2}{M}$
• C. $+\frac{\alpha v^2}{M}$
• D. $-\alpha v^2$

Answer 1

The correct option is B

$-\frac{\alpha v^2}{M}$

From Newton's second law of motion, thrust on the satellite $F=-\frac{d}{dt}\left(Mv\right)=-\left(\frac{dM}{dt}\right)v=-\alpha v^2(\because \frac{dM}{dt}=\alpha v)$
$\therefore$ Acceleration, $a=\frac{F}{m}=-\frac{\alpha v^2}{M}$
Hence, the correct choice is (b).