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.

Two spherical bodies of mass $M$ 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 collision is (in $R$)

$A$ spacecraft which is moving with a speed $u$ relative to the earth in the $x$-direction,enters the gravitational field of a much more massive planet which is moving with a speed $3u$ in the negative $x$-direction. The spacecraft exits following the trajectory as shown below. The speed of the spacecraft with respect to the earth a long time after it has escaped the planet's gravity is given by

The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

Which of the following astronomers first proposed that the Sun is static and the Earth revolves around the Sun?

$A$ particle of mass $M$ is at a distance $a$ from the surface of a thin spherical shell of equal mass $M$ and radius $a$. Which of the following statements is correct regarding the gravitational field and potential inside the shell?