$A$ man can jump to a height of $1.5 \, m$ on a planet $A$. What is the height he may be able to jump on another planet whose density and radius are,respectively,one-quarter and one-third that of planet $A$?

$A$ 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 $N$)?

If a planet has a mass and radius both half that of the Earth,the acceleration due to gravity at its surface would be ......... $m/s^2$ ($g$ on Earth $= 9.8\, m/s^2$)

The diameters of two planets are in the ratio $4:1$. Their mean densities have the ratio $1:2$. The ratio of gravitational acceleration on the surface of the planets will be:

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?

State the values of $g$ and $G$ at the center of the Earth. Identify which of $g$ and $G$ is a vector and which is a scalar.