Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e., but the force still remains a central force, then:
1. | Kepler's law of areas still holds |
2. | Kepler's law of period still holds |
3. | Kepler's law of areas and period still hold |
4. | Neither the law of areas nor the law of period still hold |
The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is:
1. | \(5^{3/2}\) years | 2. | \(5^{2/3}\) years |
3. | \(5^{1/3}\) years | 4. | \(5^{1/2}\) years |
Two satellites A and B go around the earth in circular orbits at heights of respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius , the ratio of the magnitudes of their orbital velocities is:
1.
2.
3.
4.
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 body of mass m kg starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface, is:
[R - Radius of Earth, M - Mass of Earth, G - Gravitational Constant] -
1.
2.
3.
4.
A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. R/3
2. R/2
3. R/4
4. R/5
A satellite is launched into a circular orbit of radius R around the Earth while a second satellite is launched into an orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is:
1. | 0.7 | 2. | 1.0 |
3. | 1.5 | 4. | 3 |
If the gravitational force between two objects were proportional to \(\frac{1}{R}\) (and not as ) where \(R\) is the separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to:
1.
2.
3.
4. \(1/R\)
If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then:
1. d=0.5 km
2. d=1 km
3. d=1.5 km
4. d=2 km
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 |