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

The Correct Option is D

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