The dependence of acceleration due to gravity 'g' on the distance 'r' from the centre of the earth, assumed to be a sphere of radius R of uniform density, is as shown in figure below:
The correct figure is:
1. a
2. b
3. c
4. d
The additional kinetic energy to be provided to a satellite of mass \(m\) revolving around a planet of mass \(M,\) to transfer it from a circular orbit of radius \(R_1\) to another of radius \(R_2\) (\(R_2>R_1\)) is:
1. \(GmM\)
2. \(2GmM\)
3.
4. \(GmM\)
A particle of mass M is situated at the centre of a spherical shell of the same mass and radius a. The magnitude of the gravitational potential at a point situated at a/2 distance from the centre will be:
1.
2.
3.
4.
A particle of mass \(\mathrm{m}\) is thrown upwards from the surface of the earth, with a velocity \(\mathrm{u}\). The mass and the radius of the earth are, respectively, \(\mathrm{M}\) and \(\mathrm{R}\). \(\mathrm{G}\) is the gravitational constant and \(\mathrm{g}\) is the acceleration due to gravity on the surface of the earth. The minimum value of \(\mathrm{u}\) so that the particle does not return back to earth is:
1. \(\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}^2}} \)
2. \(\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \)
3.\(\sqrt{\frac{2 \mathrm{gM}}{\mathrm{R}^2}} \)
4. \(\sqrt{ \mathrm{2gR^2}}\)
Which one of the following plots represents the variation of a gravitational field on a particle with distance \(r\) due to a thin spherical shell of radius \(R?\)
(\(r\) is measured from the centre of the spherical shell)
1. | 2. | ||
3. | 4. |
If is the escape velocity and is the orbital velocity of a satellite for orbit close to the earth's surface, then these are related by:
1. | \(v_o=v_e\) | 2. | \(v_e=\sqrt{2v_o}\) |
3. | \(v_e=\sqrt{2}~v_o\) | 4. | \(v_o=\sqrt{2}~v_e\) |
When a body of weight 72 N moves from the surface of the Earth at a height half of the radius of the earth, then the gravitational force exerted on it will be:
1. 36 N
2. 32 N
3. 144 N
4. 50 N
For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is:
1.
2. \(2\)
3.
4.
Imagine a new planet having the same density as that of the Earth but 3 times bigger than the Earth in size. If the acceleration due to gravity on the surface of the earth is g and that on the surface of the new planet is g', then:
1. | g' = 3g | 2. | g' = 9g |
3. | g' = g/9 | 4. | g' = 27g |
For a planet having mass equal to the mass of the earth but radius equal to one-fourth of the radius of the earth, its escape velocity will be:
1. | 11.2 km/s | 2. | 22.4 km/s |
3. | 5.6 km/s | 4. | 44.8 km/s |