Q. No.Both the earth and the moon are subject to gravitational force of the sun. As observed from the sun, the orbit of the moon:
1.
will be elliptical
2.
will not be strictly elliptical because the total gravitational force on it is not central
3.
is not elliptical but will necessarily be a closed curve
4.
deviates considerably from being elliptical due to the influence of planets other than the earth
If the sun and the planets carried huge amounts of opposite charges, then:
| a. | all three of Kepler’s laws would still be valid |
| b. | only the third law would be valid |
| c. | the second law would not change |
| d. | the first law would still be valid |
Which of the above statements is/are correct?
1. (a, b, c)
2. (a, d)
3. (b, c, d)
4. (a, c, d)
The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity:
| 1. | will be directed towards the centre but not the same everywhere. |
| 2. | will have the same value everywhere but not directed towards the centre. |
| 3. | will be the same everywhere in magnitude directed towards the centre. |
| 4. | cannot be zero at any point. |
1. \(R \over n^2\)
2. \(R~(n-1) \over n\)
3. \(Rn \over (n-1)\)
4. \(R \over n\)
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. | \(v_o=\sqrt{2}~v_e\) |
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 |
The density of a newly discovered planet is twice that of the earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is \(R,\) the radius of the planet would be:
| 1. | \(4R\) | 2. | \(\frac{1}{4}R\) |
| 3. | \(\frac{1}{2}R\) | 4. | \(2R\) |
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
For moon, its mass is 1/81 of Earth's mass and its diameter is 1/3.7 of Earth's diameter. If acceleration due to gravity at Earth's surface is 9.8 m/, then at the moon, its value is:
| 1. | 2.86 m/s2 | 2. | 1.65 m/s2 |
| 3. | 8.65 m/s2 | 4. | 5.16 m/s2 |
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