Gravitation Ques 53
53. A satellite in force free space sweeps stationary interplanetary dust at a rate $dM / dt=\alpha v$ where $M$ is the mass and $v$ is the velocity of the satellite and $\alpha$ is a constant. What is the deceleration of the satellite?
[1994]
(a) $-\alpha v^{2}$
(b) $-\alpha v^{2} / 2$ $ M$
(c) $-\alpha v^{2} / 2$ $ M$
(d) $-2 \alpha v^{2} /$ $ M$
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Answer:
Correct Answer: 53.(c)
Solution:
$ \begin{aligned} & \text{ (c) } F=(\frac{d M}{d t}) v=\alpha v^{2} \quad(\because \frac{d M}{d t}=\alpha v) \\ & \therefore \text{ Retardation }=\frac{-F}{M}=-\frac{\alpha v^{2}}{M} \end{aligned} $
BETA
