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:
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2.
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4. \(1/R\)
Assertion (A): | The orbit of a satellite is within the gravitational field of earth whereas escaping is beyond the gravitational field of earth. |
Reason (R): | The orbital velocity of a satellite is greater than its escape velocity. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
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 |
Rohini satellite is at a height of 500 km and Insat-B is at a height of 3600 km from the surface of the earth. The relation between their orbital velocity (\(v_R,~v_i\)) is:
1. \(v_R>v_i\)
2. \(v_R<v_i\)
3. \(v_R=v_i\)
4. No relation
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. | \(v_o=\sqrt{2}~v_e\) |
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:
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4.
Two particles of equal masses go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:
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4.
The radii of the circular orbits of two satellites A and B of the earth are \(4R\) and \(R,\) respectively. If the speed of satellite A is \(3v,\) then the speed of satellite B will be:
1. | \(3v/4\) | 2. | \(6v\) |
3. | \(12v\) | 4. | \(3v/2\) |
A satellite S is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:
1. | The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant. |
2. | The total mechanical energy of S varies periodically with time. |
3. | The linear momentum of S remains constant in magnitude. |
4. | The acceleration of S is always directed towards the centre of the earth. |
A satellite is revolving around the earth with speed . If it is stopped suddenly, then with what velocity will the satellite hit the ground? ( = escape velocity from the earth's surface)
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