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:

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:

Take the effect of bulging of earth and its rotation in account. Consider the following statements:

The time period of an earth satellite in circular orbit is independent of:

The magnitude of 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.

1. U < K

2. U > K

3. U = K

4.

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:

A person sitting in a chair in a satellite feels weightless because:

A body is suspended from a spring balance kept in a satellite. The reading of the balance is W₁ when the satellite goes in an orbit of radius R and is W₂ when it goes in an orbit of radius 2R.

1. W₁ = W₂

2. W₁ < W₂

3. W₁ > W₂

4. W₁ ≠  W₂