Q. No.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. | 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. |
| 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)
| 1. | \(\dfrac R {n^2}\) | 2. | \(\dfrac {R~(n-1)} n\) |
| 3. | \(\dfrac {Rn} { (n-1)}\) | 4. | \(\dfrac R n\) |
| 1. | \(v_o=v_e\) | 2. | \(v_e=\sqrt{2v_o}\) |
| 3. | \(v_e=\sqrt{2}~v_o\) | 4. | \(v_o=\sqrt{2}~v_e\) |
| 1. | \(g' = 3g\) | 2. | \(g' = 9g\) |
| 3. | \(g' = \frac{g}{9}\) | 4. | \(g' = 27g\) |
| 1. | \(11.2~\text{km/s}\) | 2. | \(22.4~\text{km/s}\) |
| 3. | \(5.6~\text{km/s}\) | 4. | \(44.8~\text{km/s}\) |
The density of a newly discovered planet is twice that of Earth. If the acceleration due to gravity on its surface is the same as that on Earth, and the radius of Earth is \(R,\) what will be the radius of the new planet?
| 1. | \(4R\) | 2. | \(\dfrac{1}{4}R\) |
| 3. | \(\dfrac{1}{2}R\) | 4. | \(2R\) |
The universal gravitational constant is dimensionally represented as:
1. \(\left[ML^2T^{-1}\right]\)
2. \(\left[M^{-2}L^3T^{-2}\right]\)
3. \(\left[M^{-2}L^2T^{-1}\right]\)
4. \(\left[M^{-1}L^3T^{-2}\right]\)
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
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