SATHEE: Gravitation Question 348

Gravitation Question 348

Question: A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Options:

A) $[\frac{g R^{2}}{R + x}]$

B) $[\frac{g R^{2}}{R - x}]$

C) $[g x]$

D) $[{(\frac{g R^{2}}{R + x})}^{1 / 2}]$

Show Answer

Answer:

Correct Answer: D

Solution:

Gravitational force provides the necessary centripetal force.

$[∴ \frac{m v^{2}}{(R + x)} = \frac{G m M}{{(R + x)}^{2}} a l s o,, g = \frac{G M}{R^{2}}]$

$[∴ \frac{m v^{2}}{(R + x)} = m (\frac{G M}{R^{2}}) \frac{R^{2}}{{(R + x)}^{2}} \frac{n!}{r! (n - r)!}]$

$[∴ \frac{m v^{2}}{(R + x)} = m g \frac{R^{2}}{{(R + x)}^{2}}]$

$[∴ v^{2} = \frac{g R^{2}}{R + x} \Rightarrow v = {(\frac{g R^{2}}{R + x})}^{1 / 2}]$

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Gravitation Question 348

Question: A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Options:

Answer:

Solution:

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