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)

$A$ particle of mass $m$ starts from rest at a distance $R$ from the centre and along the axis of a fixed ring of radius $R$ and mass $M$. Its velocity at the centre of the ring is:

Suppose,the acceleration due to gravity at the earth's surface is $10 \, m/s^2$ and at the surface of Mars it is $4.0 \, m/s^2$. $A$ $60 \, kg$ passenger goes from the earth to the Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the figure best represents the weight (net gravitational force) of the passenger as a function of time?

Match the $\text{LIST-I}$ with $\text{LIST-II}$:

$\text{LIST-I}$	$\text{LIST-II}$
$A$. Gravitational constant	$I$. $[LT^{-2}]$
$B$. Gravitational potential energy	$II$. $[L^2 T^{-2}]$
$C$. Gravitational potential	$III$. $[ML^2 T^{-2}]$
$D$. Acceleration due to gravity	$IV$. $[M^{-1} L^3 T^{-2}]$

Choose the correct answer from the options given below:

$A$ body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

If two bodies $A$ and $B$ of equal masses $M$ are situated in air at a distance $d$ and the gravitational force between them is $F$. Now,$50 \%$ of the mass is transferred from body $A$ to $B$ and the distance between them is reduced to $\frac{d}{2}$. If the space around them is now filled with a liquid of specific density $3$,what will be the new gravitational force?