Q. No.Two satellites of Earth, \(S_1\), and \(S_2\), are moving in the same orbit. The mass of \(S_1\) is four times the mass of \(S_2\). Which one of the following statements is true?
| 1. | The time period of \(S_1\) is four times that of \(S_2\). |
| 2. | The potential energies of the earth and satellite in the two cases are equal. |
| 3. | \(S_1\) and \(S_2\) are moving at the same speed. |
| 4. | The kinetic energies of the two satellites are equal. |
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A planet is revolving around a massive star in a circular orbit of radius \(R\). If the gravitational force of attraction between the planet and the star is inversely proportional to \(R^3,\) then the time period of revolution \(T\) is proportional to:
1. \(R^5\)
2. \(R^3\)
3. \(R^2\)
4. \(R\)
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A satellite is moving very close to a planet of density \(\rho.\) The time period of the satellite is:
1. \(\sqrt{\frac{3 \pi}{ρG}}\)
2. \(\left(\frac{3 \pi}{ρG}\right)^{3 / 2}\)
3. \(\sqrt{\frac{3 \pi}{2 ρG}}\)
4. \(\left(\frac{3 \pi}{2 ρG}\right)^{3 / 2}\)
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Magnitude of potential energy (\(U\)) and time period \((T)\) of a satellite are related to each other as:
1. \(T^2\propto \frac{1}{U^{3}}\)
2. \(T\propto \frac{1}{U^{3}}\)
3. \(T^2\propto U^3\)
4. \(T^2\propto \frac{1}{U^{2}}\)
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A satellite of mass \(m\) revolving around the earth in a circular orbit of radius \(r\) has its angular momentum equal to \(L\) about the centre of the earth. The potential energy of the satellite is:
1. \(- \frac{L^{2}}{2 mr}\)
2. \(- \frac{2L^{2}}{mr^2}\)
3. \(- \frac{3L^{2}}{m^2r^2}\)
4. \(- \frac{L^{2}}{mr^2}\)
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If the speed of an artificial satellite revolving around the earth in a circular orbit be \(2 \over 3\) of the escape velocity from the surface of earth then its altitude above the surface of the earth is
| 1. | \({4 \over 5 }R\) | 2. | \({2 \over 5 }R\) |
| 3. | \({1 \over 8 }R\) | 4. | \({3 \over 5 }R\) |
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Two astronauts are floating in a gravity free space after having lost contact with their spaceship. The two will:
| 1. | keep floating at the same distance between them |
| 2. | move towards each other |
| 3. | move away from each other |
| 4. | will become stationary |
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| 1. | \(16L\) | 2. | \(64L\) |
| 3. | \(L \over 4\) | 4. | \(4L\) |
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| 1. | \(T\) is conserved |
| 2. | \(V\) is always positive |
| 3. | \(E\) is always negative |
| 4. | the magnitude of \(L\) is conserved but its direction changes continuously |
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The centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to \(F\). The net force on the satellite is:
1. zero
2. \(F\)
3. \(F\sqrt{2}\)
4. \(2F\)
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