Q. No.| 1. | \(-Gm \over {l}^2\) | 2. | \(-Gm^2 \over 2{l}\) |
| 3. | \(-2Gm^2 \over {l}\) | 4. | \(-3Gm^2 \over {l}\) |
1. \(-E_0\)
2. \(1.5E_0\)
3. \(2E_0\)
4. \(E_0\)
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. | \(\dfrac{mg_0R^2}{2(R+h)}\) | 2. | \(-\dfrac{mg_0R^2}{2(R+h)}\) |
| 3. | \(\dfrac{2mg_0R^2}{(R+h)}\) | 4. | \(-\dfrac{2mg_0R^2}{(R+h)}\) |
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. | \(2mgR\) |
| 1. | \(\frac{GMm}{12R} \) | 2. | \(\frac{GMm}{R} \) |
| 3. | \(\frac{GMm}{8 R} \) | 4. | \(\frac{GMm}{2R}\) |
| 1. | \(mgR_e\) | 2. | \(2mgR_e\) |
| 3. | \(\frac{mgR_e}{5}\) | 4. | \(\frac{mgR_e}{16}\) |
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. \(mgR\left(\frac{n}{n+1}\right)\)
Three equal masses \(m\) are placed at the three vertices of an equilateral triangle of sides \(r.\) The 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 |
| 1. | \(-0.5\) MJ | 2. | \(-25\) MJ |
| 3. | \(-5\) MJ | 4. | \(-2.5\) MJ |
If a particle is dropped from a height \(h = 3R\) from the Earth's surface, the speed with which the particle will strike the ground is:
1. \(\sqrt{3gR}\)
2. \(\sqrt{2gR}\)
3. \(\sqrt{1.5gR}\)
4. \(\sqrt{gR}\)
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