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