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:

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

1. will be less than v_e

2. will be more than v_e

3. will be equal to v_e

4. will depend on direction of projection

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

Inside a uniform spherical shell:

Choose the correct option:

A uniform spherical shell gradually shrinks maintaining its shape. The gravitational potential at the centre

1. increases

2. decreases

3. remains constant

4. oscillates

Consider a planet moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun:

Choose the correct option: