Q. A satellite in force-free space sweeps stationary interplanetary dust at rate $\frac{dM}{dt} = \alpha\ v,\ $ where M is the mass, v is the velocity of satellite and α is a constant What is the deceleration of the satellite?
A) $\frac{- 2\alpha v^{2}}{M}$
B) $- \alpha v^{2}/M$
C) $- \alpha v^{2}$
D) $\frac{\alpha\ v^{2}}{M}$
Explanation
(d) $Force\ \ \ F = \frac{dp}{dt}$
$= v\left\lbrack \frac{dM}{dt} \right\rbrack$
$= \alpha\ v^{2}$
$\therefore\ \ \ a = \frac{F}{M} = \frac{\alpha\ v^{2}}{M}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.