The value of acceleration due to gravity at a depth $d$ from the surface of the Earth and at an altitude $h$ from the surface of the Earth are in the ratio:

If the mass of Earth is $80$ times that of a planet and its diameter is double that of the planet,and $g$ on Earth is $9.8 \ m/s^2$,then the value of $g$ on that planet is ........ $m/s^2$.

$A$ narrow but tall cabin is falling freely near the earth's surface. Inside the cabin,two small stones $A$ and $B$ are released from rest (relative to the cabin). Initially $A$ is much above the centre of mass and $B$ is much below the centre of mass of the cabin. $A$ close observation of the motion of $A$ and $B$ will reveal that

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of the earth. When both $d$ and $h$ are much smaller than the radius of the earth,then which one of the following is correct?

Where will it be profitable to purchase $1$ kilogram of sugar?

$A$ boy weighs $72 \ N$ on the surface of the earth. What will be the gravitational force on the boy at a height equal to half the radius of the earth (in $N$)?