Mark the correct statement:
$(i)$ Escape velocity does not depend on the mass of the body.
$(ii)$ If the total energy of a satellite becomes positive,it escapes from the Earth.
$(iii)$ The orbit of a geostationary satellite is called a parking orbit.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$: The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements,choose the most appropriate answer from the options given below:

Statement $(A)$ Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement $(B)$ The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement $(C)$ The escape velocity of a body is independent of the altitude of the point of projection.

Suppose the acceleration due to gravity at the earth’s surface is $g \text{ m/s}^2$ and at the surface of the moon it is $g' \text{ m/s}^2$. An $M \text{ kg}$ passenger travels from the earth to the moon in a spaceship moving with a constant velocity. Neglecting all other celestial objects, which curve best represents the net gravitational force on the passenger as a function of time?

Two particles of equal mass $m$ go round a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

The ratio of the $K.E.$ required to be given to a satellite to escape Earth's gravitational field to the $K.E.$ required to be given so that the satellite moves in a circular orbit just above Earth's atmosphere is: