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. |
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 |
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. |
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. |
Assertion (A): | \(E_0,\) then its potential energy is \(-E_0.\) | A satellite moving in a circular orbit around the earth has a total energy
Reason (R): | \(\frac{-GMm}{R}\). | Potential energy of the body at a point in a gravitational field of orbit is
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. |
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. |
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. |
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. |
Assertion (A): | Generally the path of a projectile from the Earth is parabolic but it is elliptical for a projectile going to a very great height. |
Reason (R): | At the ordinary height, the projectile moves under a uniform gravitational force, but for great heights, the projectile moves under a variable force. |
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. |
Assertion (A): | The angular velocity of a planet orbiting around the sun increases when it is nearest to the sun. |
Reason (R): | Angular momentum of a body is proportional to angular 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. |