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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. | \(\frac{mg_0R^2}{2(R+h)}\) | 2. | \(-\frac{mg_0R^2}{2(R+h)}\) |
| 3. | \(\frac{2mg_0R^2}{(R+h)}\) | 4. | \(-\frac{2mg_0R^2}{(R+h)}\) |
| 1. | \(mgR_e\) | 2. | \(2mgR_e\) |
| 3. | \(\frac{mgR_e}{5}\) | 4. | \(\frac{mgR_e}{16}\) |
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 |
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. \(\sqrt{gR}\)
A rocket of mass \(M\) is launched vertically from the surface of the earth with an initial speed \(v\). Assuming the radius of the earth to be \(R\) and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is:
1. \(\frac{R}{\left(\frac{gR}{2v^2}-1\right)}\)
2. \(R\left({\frac{gR}{2v^2}-1}\right)\)
3. \(\frac{R}{\left(\frac{2gR}{v^2}-1\right)}\)
4. \(R{\left(\frac{2gR}{v^2}-1\right)}\)
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