A remote sensing satellite of the earth revolves in a circular orbit at a height of $0.25 \times10^6~\text{m}$ above the surface of the earth. If Earth’s radius is $6.38\times10^6~\text{m}$ and $g=9.8~\text{ms}^{-2},$ then the orbital speed of the satellite is:
1. $7.76~\text{kms}^{-1}$
2. $8.56~\text{kms}^{-1}$
3. $9.13~\text{kms}^{-1}$
4. $6.67~\text{kms}^{-1}$

A satellite $S$ is moving in an elliptical orbit around the Earth. If the mass of the satellite is very small as compared to the mass of the earth, then:

Kepler's third law states that the square of the period of revolution ($T$) of a planet around the sun, is proportional to the third power of average distance $r$ between the sun and planet i.e. $T^2 = Kr^3$, here $K$ is constant. If the masses of the sun and planet are $M$ and $m$ respectively, then as per Newton's law of gravitation, the force of attraction between them is $F = \frac{GMm}{r^2},$ here $G$ is the gravitational constant. The relation between $G$ and $K$ is described as:
1. $GK = 4\pi^2$
2. $GMK = 4\pi^2$
3. $K =G$
4. $K = \frac{1}{G}$

Two spherical bodies of masses $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R.$ If they attract each other due to gravitational force only, then the distance covered by the smaller body before the collision is:

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass$m=5.98\times 10^{24}~\text{kg})$ have to be compressed to be a black hole?
1. $10^{-9}~\text{m}$
2. $10^{-6}~\text{m}$
3. $10^{-2}~\text{m}$
4. $100​~\text{m}$

Dependence of intensity of gravitational field $(\mathrm{E})$ of the earth with distance $(\mathrm{r})$ from the centre of the earth is correctly represented by: (where $\mathrm{R}$ is the radius of the earth)

1.		2.
3.		4.

A body of mass $m$ is taken from the Earth’s surface to the height equal to twice the radius $(R)$ of the Earth. The change in potential energy of the body will be: