A projectile is fired upwards from the surface of the earth with a velocity where is the escape velocity and k < 1. If r is the maximum distance from the center of the earth to which it rises and R is the radius of the earth, then r equals:
1. \(\frac{R}{k^2}\)
2. \(\frac{R}{1-k^2}\)
3. \(\frac{2R}{1-k^2}\)
4. \(\frac{2R}{1+k^2}\)
If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:
1. | \(\frac{M}{A}\) | 2. | \(2MA\) |
3. | \(A^2M\) | 4. | \(AM^2\) |
Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:
1.
2.
3.
4.
For the moon to cease as the earth's satellite, its orbital velocity has to be increased by a factor of -
1. | 2 | 2. | \(\sqrt{2}\) |
3. | \(1/\sqrt{2}\) | 4. | 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 \(d_1\) and \(d_2\) from the sun and their frequencies are \(n_1\) and \(n_2\) respectively, then:
1. \(n^2_1d^2_1= n_2d^2_2\)
2. \(n^2_2d^3_2= n^2_1d^3_1\)
3. \(n_1d^2_1= n_2d^2_2\)
4. \(n^2_1d_1= n^2_2d_2\)
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.
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
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. \(1/R\)