Question 1 :
If a planet gets inflated, keeping its density constant, then $g$ will increase.

Question 2 :
Find the relation between the gravitational field on the surface of two planets A and B of masses $m_A, m_B$ and radii $R_A$ and $R_B$, respectively, if<br>a. they have equal mass,<br>b. they have equal (uniform) density.<br>

Question 3 :
Two satellites $S_1 \, and \, S_2$ revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hr and 8 hr respectively. The radius of the orbit of $S_1 \, is \, 10^4 \, km$. When $S_2$ is closest to $S_1$ find the angular speed of $S_2$ as actually observed by an astronaut in $S_1$.

Question 4 :
Both earth and moon are subject to the gravitational force to the sun. As observed from the sun, the orbit of the moon

Question 5 :
A body is moving around sun in an elliptical orbit.The maximum and minimum distance are $3 \times 10^{12} m \,\, and \,\, 2 \times 10^{10}m$. The velocity at minimum distance is $2 \times 10^7 m/sec$. Find the velocity of the body at maximum distance.

Question 6 :
Two planets $A$ and $B$ have their radii in the ratio of $2 : 5$ and densities in the ratio of $1 : 6$ respectively. Which of the following statements is NOT true regarding the given information?

Question 7 :
The distance of Venus from the sun is $0.72\ AU$. the orbital period of the Venus is

Question 8 :
A communication satellite of earth which takes $24 hr$. to complete one circular orbit eventually has to be replaced by another satellite of double mass. If the new satellites also has an orbital time period of $24 hrs$, then what is the ratio of the radius of the new orbit to the original orbit ?

Question 9 :
Two ordinary satellites are revolving round the Earth in same elliptical orbit, then which of the following quantities is conserved<br/>

Question 10 :
The height of a point vertically above the earth's surface at which the acceleration due to gravity becomes $9\%$ of its value at the surface is (Given, R$=$ radius of earth)