The weight of an object in a coal mine,at sea level,and at the top of a mountain are $W_1$,$W_2$,and $W_3$ respectively. Then:

The diameters of two planets are in the ratio $4 : 1$ and their mean densities in the ratio $1 : 2$. The acceleration due to gravity on the planets will be in the ratio:

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of the Earth of radius $R$. If $r < R$,then:

$A$ body has a weight of $90 \ kgf$ on the earth's surface. The mass of the moon is $1/9$ of the earth's mass and its radius is $1/2$ of the earth's radius. On the moon,the weight of the body is .......... $kgf$.

The mass of a planet is $\frac{1}{10}$ that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is: (in $m \ s^{-2}$)

$A$ certain planet completes one rotation about its axis in time $T$. The weight of an object placed at the equator on the planet's surface is a fraction $f$ ($f$ is close to unity) of its weight recorded at a latitude of $60^{\circ}$. The density of the planet (assumed to be a uniform perfect sphere) is given by