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 acceleration of satellite is

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

Answer 1

Answer: (D)

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

Answer 2

Rate of change of mass $\frac{dM}{dt} = \alpha v$.
Retarding force = Rate of change of momentum
= Velocity x Rate of change in mass = $-v \times \frac{dM}{dt}$
$= - v \times \alpha v = - \alpha v^2 .$ (Minus sign of v due to deceleration)
Therefore Acceleration $= \frac{-\alpha v^2}{ M}$.