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

Answer 1

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

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, $\frac{dM}{dt}=\alpha v$
since, $F=0$ , we have acceleration $\frac{dv}{dt}=\frac{\alpha v^2}{M}$
The deceleration of the satellite. $=-\frac{\alpha v^2}{M}$
hence,option C is correct.