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The critical velocity required for a satellite to revolve in a given orbit depends on which of the following?
AThe radius of the orbit but not the satellite's mass
BThe satellite's mass but not the orbit radius
CBoth the satellite's mass and the orbit radius
DNeither the satellite's mass nor the orbit radius
Answer & Solution
Correct answer: A. The radius of the orbit but not the satellite's mass
1. From $\dfrac{mv_c^2}{R+h} = \dfrac{GMm}{(R+h)^2}$, the satellite mass $m$ cancels from both sides.
2. This leaves $v_c = \sqrt{\dfrac{GM}{R+h}}$, which contains only $G$, the earth's mass $M$, and the orbital radius $R+h$.
3. So the critical velocity does not depend on the satellite's own mass (rule out options naming mass).
4. It depends on the orbit radius $R+h$. Hence option A is correct.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 10 "Space Missions", p.147_
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