Gravitation - Result Question 53

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56. 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?

======= ####56. 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?

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/gravitation/gravitation—result-question-53.md (a) $-\alpha v^{2}$

(b) $-\alpha v^{2} / 2 M$

(c) $-\alpha v^{2} / 2 M$

(d) $-2 \alpha v^{2} / M$

[1994]

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Answer:

Correct Answer: 56. (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} $