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)

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