The gravitational potential energy of an isolated system of three particles, each of mass \(m\) placed at three corners of an equilateral triangle of side \(l\) is: 
1. \(-Gm \over {l}^2\) 2. \(-Gm^2 \over 2{l}\)
3. \(-2Gm^2 \over {l}\) 4. \(-3Gm^2 \over {l}\)
Subtopic:  Gravitational Potential Energy |
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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy \(E_0\). Its potential energy is?
1. \(-E_0\)
2. \(1.5E_0\)
3. \(2E_0\)
4. \(E_0\)
Subtopic:  Gravitational Potential Energy |
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A satellite of mass \(m\) is orbiting the earth (of radius \(R\)) at a height \(h\) from its surface. What is the total energy of the satellite in terms of \(g_0?\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)

1. \(\frac{mg_0R^2}{2(R+h)}\) 2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{(R+h)}\) 4. \(-\frac{2mg_0R^2}{(R+h)}\)
Subtopic:  Gravitational Potential Energy |
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The energy required to move a satellite of mass \(m\) from an orbit of radius \(2R\) to \(3R\) around the Earth having mass \(M\) is:
1. \(\frac{GMm}{12R} \) 2. \(\frac{GMm}{R} \)
3. \(\frac{GMm}{8 R} \) 4. \(\frac{GMm}{2R}\)
Subtopic:  Gravitational Potential Energy |
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A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be: 

1. \(\frac{2}{3}mgR\) 2. \(3mgR\)
3. \(\frac{1}{3}mgR\) 4. \(2mgR\)
Subtopic:  Gravitational Potential Energy |
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The change in the potential energy, when a body of mass \(m\) is raised to a height \(nR\) from the Earth's surface is: (\(R\) = Radius of the Earth)
1. \(mgR\left(\frac{n}{n-1}\right)\)
2. \(nmgR\)
3. \(mgR\left(\frac{n^2}{n^2+1}\right)\)
4. \(mgR\left(\frac{n}{n+1}\right)\)

Subtopic:  Gravitational Potential Energy |
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A body of mass \(m\) is situated at a distance \(4R_e\) above the Earth's surface, where \(R_e\) is the radius of the Earth. What minimum energy should be given to the body so that it may escape? 
1. \(mgR_e\) 2. \(2mgR_e\)
3. \(\frac{mgR_e}{5}\) 4. \(\frac{mgR_e}{16}\)
Subtopic:  Gravitational Potential Energy |
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A satellite of mass \(1000\) kg revolves in a circular orbit around the earth with a constant speed of \(100\) m/s. The total mechanical energy of the satellite is:
1. \(-0.5\) MJ 2. \(-25\) MJ
3. \(-5\) MJ 4. \(-2.5\) MJ
Subtopic:  Gravitational Potential Energy |
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Three equal masses \(m\) are placed at the three vertices of an equilateral triangle of side \(r\). Work required to double the separation between masses will be:

                      

1. \(Gm^2\over r\) 2. \(3Gm^2\over r\)
3. \({3 \over 2}{Gm^2\over r}\) 4. None of the above
Subtopic:  Gravitational Potential Energy |
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Given below are two statements: 
Assertion (A): A satellite moving in a circular orbit around the earth has a total energy \(E_0,\) then its potential energy is \(-E_0.\)
Reason (R): Potential energy of the body at a point in a gravitational field of orbit is \(\frac{-GMm}{R}\).
 
1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. (A) is False but (R) is True.
Subtopic:  Gravitational Potential Energy |
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