Question

A satellite in 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 tangential acceleration of satellite is

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

Answer 1

Answer: (C)

we know $F=\frac{d}{dt}\left(Mv\right)=M\frac{dv}{dt}+v\frac{dM}{dt}=M\frac{dv}{dt}+v\alpha v$ As, $\frac{dM}{dt}=\alpha v$