A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? (Mass of the space ship = 1000 kg; mass of the sun = 2×${10}^{30}$ kg; mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28×${10}^8$ km; G = 6.67×${10}^{-11}$$N m^2 k{g}^{-2}$.)
1. 11 × 10¹⁰ J
2. 6 × 10¹¹ J
3. 6.67 × 10¹⁰ J
4. 7.12 × 10¹¹ J

A rocket is fired vertically from the surface of mars with a speed of 2 km/s. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it?

(Mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; G = 6.67×${10}^{-11}$ $N m^2 k{g}^{-2}.$)

1. 477.2 km
2. 550.5 km
3. 493.9 km
4. 517.3 km

According to Kepler, the planets move in:

1. the circular orbits around the sun with the sun at its center.

2. the elliptical orbits around the sun.

3. the straight lines with constant velocity.

4. the elliptical orbits around the sun with the sun at one of its foci.

The minimum and maximum distances of a planet revolving around the sun are r and R. If the minimum speed of the planet on its trajectory is v₀, its maximum speed will be:

1. $\frac{{\mathrm{v}}_0\mathrm{R}}{\mathrm{r}}$

2. $\frac{{\mathrm{v}}_0\mathrm{r}}{\mathrm{R}}$

3. $\frac{{\mathrm{v}}_0{\mathrm{R}}^2}{{\mathrm{r}}^2}$

4. $\frac{{\mathrm{v}}_0{\mathrm{r}}^2}{{\mathrm{R}}^2}$

The torque on a planet about the centre of the sun is:

1. zero.

2. negative.

3. positive.

4. dependent on the mass of the planet.

During the motion of a planet from perihelion to aphelion, the work done by the gravitational force of the sun on it is:

1. zero.

2. negative.

3. positive.

4. may be positive or negative.

The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit of radius 4R is:

1. 4T

2. $\frac{\mathrm{T}}{4}$

3. 8T

4. $\frac{\mathrm{T}}{8}$

Gravitation is the phenomenon of interaction between:

1. Point masses only

2. Any arbitrarily shaped masses

3. Planets only

4. None of these

The Force of gravitation between two masses is found to be F in a vacuum. If both the masses are dipped in water at the same distance, then the new force will be:

1. >F

2. <F

3. F

4. Cannot say

Two-point masses m and 4m are separated by a distance d on a line. A third point mass m₀ is to be placed at a point on the line such that the net gravitational force on it is equal to zero.

The distance of that point from the mass m is:

1. $\frac{\mathrm{d}}{2}$

2. $\frac{\mathrm{d}}{4}$

3. $\frac{\mathrm{d}}{3}$

4. $\frac{\mathrm{d}}{5}$