Select the correct option based on statements below:

 Assertion (A): The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason (R): The product of their mass and radius must be same, $$M_1R_1=M_2R_2.$$

 1 Both (A) and (R) are correct but (R) is not the correct explanation of (A). 2 (A) is correct but (R) is not correct. 3 Both (A) and (R) are correct and (R) is the correct explanation of (A). 4 (A) is not correct but (R) is correct.
Subtopic: Â Escape velocity |
Â 67%
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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:

 (A): The plot of V against r is discontinuous. (B): The plot of E against r is discontinuous.

 1 Both A and B are correct 2 A is correct but B is wrong 3 B is correct but A is wrong 4 Both A and B are wrong
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:

 (A) The plot of $$V$$ against $$r$$ is discontinuous. (B) The plot of $$E$$ against $$r$$ is discontinuous.

 1 Both (A) and (B) are correct. 2 (A) is correct but (B) is wrong. 3 (B) is correct but (A) is wrong. 4 Both (A) and (B) are wrong.
Subtopic: Â Gravitational Field |
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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 |
Â 52%
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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 |
Â 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 |
Â 59%
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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 |
Â 76%
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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 |
Â 63%
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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 |
Â 59%
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 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.
Subtopic: Â Orbital velocity |
Â 81%
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