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 , then the time period of revolution T is proportional to:
1.
2.
3.
4. R
A satellite is moving very close to a planet of density . The time period of the satellite is:
1.
2.
3.
4.
Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:
1.
2.
3.
4.
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. | 2. | ||
3. | 4. |
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. | \({3 \over 5 }R\) |
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 |
The orbital angular momentum of a satellite revolving at a distance \(r\)from the centre is \(L\). If the distance is increased to 16r, then the new angular momentum will be:
1. | \(16~L\) | 2. | \(64~L\) |
3. | \(L \over 4\) | 4. | \(4~L\) |
A planet is moving in an elliptical orbit. If T, V, E, and L stand, respectively, for its kinetic energy, gravitational potential energy, total energy and angular momentum about the center of the orbit, then:
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 |
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.
4. 2 F