A planet moves around the sun. At a point P, it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point Q, when it is farthest from the sun at distance \(d_2,\) its speed will be:

1.	\(d_2v_1 \over d_1\)	2.	\(d_1v_1 \over d_2\)
3.	\(d_1^2v_1 \over d_2\)	4.	\(d_2^2v_1 \over d_1\)

A satellite that is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of the earth in the new orbit is \(2\) times that of the earlier orbit. The time period in the second orbit is:
1. \(48\)$\sqrt{2}$ hr
2. \(48\) hr
3. \(24\)$\sqrt{2}$ hr
4. \(24\) hr

Acceleration due to gravity is:

Choose the correct alternative.

The time period of a geostationary satellite is 24 h, at a height of 6$R_E$ ($R_E$ is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is 2.5$R_E$ from the surface will be:

1. 6$\sqrt{2}h$

2. 12$\sqrt{2}h$

3. $\frac{24}{2.5}h$

4.  $\frac{12}{2.5}h$

The escape speed of a projectile on the earth’s surface is 11.2 km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth?  (Ignore the presence of the sun and other planets.)

1. 32.7 km/s

2. 11.2 km/s

3. 31.7 km/s

4. 21.2 km/s

The gravitational potential energy of an isolated system of three particles, each of mass \(\mathrm{m}\) placed at three corners of an equilateral triangle of side \(\mathrm{l}\) is: 

Two satellites S₁ and S₂ are revolving around a planet in coplanar and concentric circular orbits of radii R₁ and R₂ in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S₁ is equal to 10⁴ km. Find the relative speed when they are closest to each other. 

1. $2\mathrm{\pi }\times {10}^4$ $\mathrm{kmph}$

2. $\mathrm{\pi }\times {10}^4$ $\mathrm{kmph}$

3. $\frac{\mathrm{\pi }}{2}\times {10}^4$ $\mathrm{kmph}$

4. $\frac{\mathrm{\pi }}{3}\times {10}^4$ $\mathrm{kmph}$ 

The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity:
 

Both the earth and the moon are subject to gravitational force of the sun. As observed from the sun, the orbit of the moon: