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. |
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. \(R\)
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. \(T^2\propto \frac{1}{U^{2}}\)
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. \(- \frac{L^{2}}{mr^2}\)
Two astronauts are floating in a gravitational 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 |