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:

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

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:

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

The kinetic energy needed to project a body of mass m from the earth's surface to infinity is

1. \(\frac14\) mgR

2. \(\frac12\) mgR

3. mgR

4. 2 mgR

A particle is kept at rest at a distance R (earth's radius) above the earth's surface. The minimum speed with which it should be projected so that it does not return is

1. \(\sqrt\frac{GM}{4R}\)

2. \(\sqrt\frac{GM}{2R}\)

3. \(\sqrt\frac{GM}{R}\)

4. \(\sqrt\frac{2GM}{R}\)

A satellite is orbiting the earth close to its surface. A particle is to be projected from the satellite to just escape from the Earth. The escape speed from the Earth is \(v_e.\) Its speed with respect to the satellite: