Suppose the gravitational force varies inversely as the power of distance then the time period of a planet in circular orbit of radius R around the sun will be proportional to:
1.
2.
3.
4.
Time period of a satellite revolving above Earth’s surface at a height equal to \(\mathrm{R}\) (the radius of Earth) will be:
(g is the acceleration due to gravity at Earth’s surface)
1.
2.
3.
4.
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.
2.
3.
4.
If two planets are at mean distances and from the sun and their frequencies are n1 and n2 respectively, then:
1.
2.
3.
4.
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