Question

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

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

Answer 1

The correct option is D $\frac{-\alpha v^2}{M}$

$\frac{dM}{dt}=\alpha VF=\frac{d}{dt}\left(MV\right)=M\frac{dV}{dt}+V\frac{dM}{dt}=M\frac{dV}{dt}+V\left(\alpha V\right)F=0\therefore M\frac{dV}{dt}=-\alpha V^2\Rightarrow \frac{dV}{dt}=\frac{-\alpha V^2}{m}=acceleration$