Q. No.If the gravitational force between two objects were proportional to \(\frac{1}{R}\) (and not as\(\frac{1}{R^2}\)) 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. \(\frac{1}{R^2}\)
2. \(R^{0}\)
3. \(R^{1}\)
4. \(\frac{1}{R}\)
| Assertion (A): | The orbit of a satellite lies within Earth's gravitational field, while escaping occurs beyond the Earth's gravitational field. |
| 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 specific relation
| 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 \(R_A ~\text{and}~R_B\) respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius \(R_e\), the ratio of the magnitudes of their orbital velocities is:
1. \(\sqrt{\frac{R_{B}}{R_{A}}}\)
2. \(\frac{R_{B} + R_{e}}{R_{A} + R_{e}}\)
3. \(\sqrt{\frac{R_{B} + R_{e}}{R_{A} + R_{e}}}\)
4. \(\left(\frac{R_{A}}{R_{B}}\right)^{2}\)
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:
1. \(v = \frac{1}{2 R} \sqrt{\frac{1}{Gm}}\)
2. \(v = \sqrt{\frac{Gm}{2 R}}\)
3. \(v = \frac{1}{2} \sqrt{\frac{G m}{R}}\)
4. \(v = \sqrt{\frac{4 Gm}{R}}\)
The radii of the circular orbits of two satellites \(A\) and \(B\) of the earth are \(4R\) and \(R,\) respectively. If the speed of the satellite \(A\) is \(3v,\) then the speed of the 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 \(v_0\). If it is stopped suddenly, then with what velocity will the satellite hit the ground? (\(v_e\)= escape velocity from the earth's surface)
1. \(\sqrt{v_{e}^{2} - v_{0}^{2}}\)
2. \(\sqrt{v_{e}^{2}-2 v_{0}^{2}}\)
3. \(\sqrt{v_{e}^{2}-3 v_{0}^{2}}\)
4. \(\sqrt{v_{e}^{2}-\frac{v_{0}^{2}}{2}}\)
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