A satellite of mass \(M\) is revolving around the Earth in a stationary orbit with a time period \(T.\) If \(10\%\) of the satellite's mass is detached, what will happen to its time period?
1. remain the same
2. increase by \(10\%\)
3. decrease by \(10\%\)
4. decrease by \(20\%\)

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For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:

1. \(\dfrac{1}{\sqrt{2}}\)

2. \(2\)

3. \(\sqrt{2} \)

4. \(\dfrac{1}{2}\)

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The energy required to shift a satellite from orbital radius \(r\) to orbital radius \(2r\) is \(E\). What energy will be required to shift the satellite from orbital radius \(2r\) to orbital radius \(3r\)?
1. \(E\)
2. \(E/2\)
3. \(E/3\)
4. \(E/4\)
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The correct formula for the height of a satellite from Earth's surface is:

1. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi^2}\right)^{1 / 3}-{R} \)

2. \(\left(\dfrac{T^2 R^2 g}{4 \pi}\right)^{1 / 2}-R \)

3. \(\left(\dfrac{{T}^2 {R}^2}{4 \pi^2 {g}}\right)^{1 / 3}-{R}\)

4. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi}\right)^{-1 / 3}+{R}\)
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