The height at which the weight of a body becomes $\frac{1}{9}$ of its weight on the surface of the earth (radius of the earth is $R$) is:

Acceleration due to gravity $g$ for a body of mass $m$ on the Earth's surface is proportional to (Radius of Earth $= R$,mass of Earth $= M$)

The depth $d$ at which the acceleration due to gravity becomes $\frac{g}{n}$ is (where $R$ is the radius of the Earth,$g$ is the acceleration due to gravity at the surface,and $n$ is an integer).

Assuming the density of the Earth is constant, which graph correctly represents the variation of acceleration due to gravity $(g)$ with the distance $(r)$ from the center of the Earth (radius of the Earth $= R$)?

At what distance above and below the surface of the earth will a body have the same weight? (Take the radius of the earth as $R$.)

The centre of gravity of a body on the earth coincides with its centre of mass for a small object,whereas for an extended object,it may not. What is the qualitative meaning of 'small' and 'extended' in this regard? For which of the following does the centre of gravity coincide with the centre of mass: a building,a pond,a lake,a mountain?