Question

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

• A. $-3\alpha v^2/M$
• B. $-2\alpha v^2/M$
• C. $-\alpha v^2/M$
• D. $-\alpha v^2$

Answer 1

The correct option is C $-\alpha v^2/M$

Given that,

Mass of satellite = M

$\frac{dM}{dt}=+\alpha v$

Now,

Newton’s second law

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

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

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

Now, $F=0$

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

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

Hence, the acceleration of satellite is $-\frac{\alpha v^2}{M}$