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Q. No.Select the correct option based on the statements below:
| Assertion (A): | The escape velocities of planets \(A\) and \(B\) are the same. But \(A\) and \(B\) are of unequal mass. |
| Reason (R): | The product of their mass and radius must be the same, \(M_1R_1=M_2R_2.\) |
| 1. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 2. | (A) is True but (R) is False. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Escape velocity |
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Let \(V\) and \(E\) represent the gravitational potential and field at a distance \(r\) from the centre of a uniform solid sphere. Consider the two statements:
| Statement (A): | The plot of \(V\) against \(r\) is discontinuous. |
| Statement (B): | The plot of \(E\) against \(r\) is discontinuous. |
| 1. | Both Statement (A) and Statement (B) are correct |
| 2. | Statement (A) is correct but Statement (B) is incorrect |
| 3. | Statement (B) is correct but Statement (A) is incorrect |
| 4. | Both Statement (A) and Statement (B) are incorrect |
Subtopic: Â Gravitational Field |
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Let \(V\) and \(E\) be the gravitational potential and gravitational field at a distance \(r\) from the centre of a uniform spherical shell. Consider the following two statements:
| Statement (A): | The plot of \(V\) against \(r\) is discontinuous. |
| Statement (B): | The plot of \(E\) against \(r\) is discontinuous. |
| 1. | Both Statement (A) and Statement (B) are correct. |
| 2. | Statement (A) is correct but Statement (B) is incorrect. |
| 3. | Statement (B) is correct but Statement (A) is incorrect. |
| 4. | Both Statement (A) and Statement (B) are incorrect. |
Subtopic: Â Gravitational Field |
 51%
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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)
Subtopic: Â Kepler's Laws |
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Given below are two statements:
| Assertion (A): | An astronaut in an orbiting space station above the Earth experiences weightlessness. |
| Reason (R): | An object moving around the earth under the influence of the earth's gravitational forces is in a state of 'free fall'. |
| 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. |
Subtopic: Â Satellite |
 65%
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Given below are two statements:
| Assertion (A): | The satellites equipped with electronic devices are called active satellites. |
| Reason (R): | Passive satellite works as active satellite. |
| 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. | (A) is false but (R) is true. |
Subtopic: Â Satellite |
 61%
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Given below are two statements:
| Assertion (A): | A satellite moving in a circular orbit around the earth has a total energy \(E_0,\) then its potential energy is \(-E_0.\) |
| Reason (R): | Potential energy of the body at a point in a gravitational field of orbit is \(\frac{-GMm}{R}\). |
| 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. | (A) is False but (R) is True. |
Subtopic: Â Gravitational Potential Energy |
 83%
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Given below are two statements:
| Assertion (A): | There is no effect of rotation of earth on acceleration due to gravity at poles. |
| Reason (R): | Rotation of earth is about the polar axis. |
| 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. |
Subtopic: Â Acceleration due to Gravity |
 67%
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Given below are two statements:
| Assertion (A): | A tennis ball bounces higher on hills than on plains. |
| Reason (R): | Acceleration due to gravity on the hill is greater than that on the surface of the earth. |
| 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. |
Subtopic: Â Acceleration due to Gravity |
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Given below are two statements:
| 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. |
Subtopic: Â Orbital velocity |
 77%
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