$A$ particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement is

Which one of the following plots represents the variation of gravitational field on a particle with distance $r$ due to a thin spherical shell of radius $R$? ($r$ is measured from the centre of the spherical shell)

The distance between the Sun and the Earth is $1.6 \times 10^{11} \,m$ and the radius of the Earth is $6.4 \times 10^6 \,m$. The ratio of the angular momentum of the Earth around the Sun to the angular momentum around its own axis is approximately (Assume the Earth as a solid sphere with uniform mass density and that it rotates around the Sun in a circular path.)

$A$ rocket is fired vertically from the surface of Mars with a speed of $2 \; km/s$. If $20 \%$ of its initial kinetic energy is lost due to Martian atmospheric resistance,how far will the rocket go from the surface of Mars before returning to it? (Mass of Mars $= 6.4 \times 10^{23} \; kg$,radius of Mars $= 3395 \; km$,$G = 6.67 \times 10^{-11} \; N m^2 kg^{-2}$)

The correct graph representing the variation of total energy $(E_t)$,kinetic energy $(E_k)$,and potential energy $(U)$ of a satellite with its distance $(r)$ from the centre of the Earth is:

Every planet revolves around the sun in an elliptical orbit. Which of the following statements are correct?
$A.$ The force acting on a planet is inversely proportional to the square of the distance from the sun.
$B.$ The force acting on the planet is inversely proportional to the product of the masses of the planet and the sun.
$C.$ The centripetal force acting on the planet is directed away from the sun.
$D.$ The square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
Choose the correct answer from the options given below: