Q. No.Consider a planet in some solar system that has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weigh
1. W
2. 2W
3. W/2
4. 21/3W at the planet
If the acceleration due to gravity at the surface of earth is \(g,\) the work done in slowly lifting a body of mass \(m\) from the earth's surface to a height \(R\) equal to the radius of the earth is:
1. \(\frac 12\)\(mgR\)
2. \(2mgR\)
3. \(mgR\)
4. \(\frac 14\)\(mgR\)
A person brings a mass of 1 kg from infinity to a point A. Initially, the mass was at rest but it moves at a speed of 2 m s–1 as it reaches A. The work done by the person on the mass is –3 J. The potential at A is:
1. –3 J/kg–1
2. –2 J/kg–1
3. –5 J/kg–1
4. none of these
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. |
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 |
Take the effect of the bulging of the Earth and its rotation in account. Consider the following statements:
| Statement I: | There are points outside the earth where the value of \(g\) is equal to its value at the equator. |
| Statement II: | There are points outside the earth where the value of \(g\) is equal to its value at the poles. |
| 1. | Both Statement I and Statement II are correct. |
| 2. | Statement I is correct but Statement II is incorrect. |
| 3. | Statement II is correct but Statement I is incorrect. |
| 4. | Both Statement I and Statement II are incorrect. |
The time period of an earth satellite in circular orbit is independent of:
| 1. | the mass of the satellite | 2. | radius of the orbit |
| 3. | none of them | 4. | both of them |
The magnitude of the gravitational potential energy of the moon-earth system is \(U\) with zero potential energy at infinite separation. The kinetic energy of the moon with respect to the earth is \(K.\) Then:
1. \(U < K\)
2. \(U > K\)
3. \(U = K\)
4. None of these
The figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If \(t_1\) and \(t_2\) be the time taken by the planet to go from \(a\) to \(b\) and from \(c\) to \(d\) respectively, then:
| 1. | \(t_1<t_2\) |
| 2. | \(t_1=t_2\) |
| 3. | \(t_1>t_2\) |
| 4. | insufficient information between \(t_1\) and \(t_2\) |
A person sitting in a chair in a satellite feels weightless because:
| 1. | the earth does not attract the objects in a satellite. |
| 2. | the normal force by the chair on the person balances the earth's attraction. |
| 3. | the normal force is zero. |
| 4. | the person in the satellite is not accelerated. |
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