Question

Two satellites are in the parking orbits around the earth.
Mass of one is 10 times that of the other. The ratio of their
periods of revolution is:
1
A
10
B
1
C
10
10/10​

Answer 1

Answer:

The period of their revolutions is 1:1 as Time period of a revolving object is independent of the mass of that object.

Hope this helps!!!

Answer 2

Two satellites are in the parking orbits around the earth.  Mass of one is 10 times that of the other. The ratio of their  periods of revolution is 1

Therefore, Option (B) is correct.

Explanation:

The gravitational force between Earth (Mass M, radius R) and a satellite of mass m at a distance h from the surface of the Earth is given by

$F=\frac{GMm}{(R+h)^2}$

This force will be responsible for the centripetal acceleration of the satellite

Thus, if angular velocity of the satellite is ω

Then,

$m(R+h)\omega^2=\frac{GMm}{(R+h)^2}$

$\implies \omega=\sqrt{\frac{GM}{(R+h)^3}}$

Therefore, the time period of the satellite will be

$T=\frac{2\pi}{\omega}$

$\implies T=2\pi\sqrt{\frac{(R+h)^3}{GM}}$

It is clear from the above formula that the time period of a satellite does not depend on its mass

Therefore, for both the satellites in the parking orbits, the time period will remain same

Therefore, the ratio of their periods of revolution will be 1

Hope this answer is helpful.

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