Statement I: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is between the Earth and the Sun. |
Statement II: | The gravitational force exerted by the Sun on the Earth is reduced when the Moon is opposite to the Sun, relative to the Earth. |
1. | Statement I is incorrect and Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct and Statement II is incorrect. |
Assertion (A): | Gravitational potential is constant everywhere inside a spherical shell. |
Reason (R): | Gravitational field inside a spherical shell is zero everywhere. |
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. |
Statement I: | The gravitational force acting on a particle depends on the electric charge of the particle. |
Statement II: | The gravitational force on an extended body can be calculated by assuming the body to be a particle 'concentrated' at its centre of mass and applying Newton's law of gravitation. |
1. | Statement I is incorrect and Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct and Statement II is incorrect. |
1. | 2. | ||
3. | 4. |
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 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): | \(E_0,\) 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. |
A particle starts from rest at a large distance from a planet, reaches the planet solely under gravitational attraction, and passes through a smooth tunnel through its center. Which statement about the particle is/are correct?
1. | The total energy of the particle will be zero at a large distance. |
2. | The gravitational potential energy of the particle at the centre will be \(\frac{3}{2}\) times that of at the surface of the planet. |
3. | The gravitational potential energy of the particle at the centre of the plant will be zero. |
4. | Both statements (1) and (2) are correct. |
The initial velocity \(v_i\) required to project a body vertically upwards from the surface of the earth to just reach a height of \(10R\), where \(R\) is the radius of the earth, described in terms of escape velocity \(v_e\) is:
1. \(\sqrt{\frac{10}{11}}v_e\)
2. \(\sqrt{\frac{11}{10}}v_e\)
3. \(\sqrt{\frac{20}{11}}v_e\)
4. \(\sqrt{\frac{11}{20}}v_e\)
A satellite is revolving in a circular orbit at a height \(h\) from the earth's surface (radius of earth \(R\); \(h<<R\)). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field is close to: (Neglect the effect of the atmosphere.)
1. \(\sqrt{2gR}\)
2. \(\sqrt{gR}\)
3. \(\sqrt{\frac{gR}{2}}\)
4. \(\sqrt{gR}\left(\sqrt{2}-1\right)\)