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:

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:

Let V and E denote the gravitational potential and gravitational field at a point. It is possible to have:

(a) V = 0 and E = 0

(b) V = 0 and E ≠ 0

(c) V ≠ 0 and E = 0

(d) V ≠ 0 and E ≠ 0

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these