Question

A satellite in a force free space sweeps stationary interplanetary dust at a rate $\left(dM/dt\right)=\alpha v$.The acceleration of satelite is

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

Answer 1

Answer: (B)

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

The force acting on the satellite is given by:

$F=\frac{d}{dt}\left(Mv\right)$

$=\frac{dv}{dt}M+v\frac{dM}{dt}$

$=M\frac{dv}{dt}+v\left(\alpha v\right)$

We know that the net force is zero. $F=0$,

$M\frac{dv}{dt}=-v\left(\alpha v\right)$

$\frac{dv}{dt}=a=-\frac{\alpha v^2}{M}$.