In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the earth). The value of OA $: AB$ will be $x : y .$ The value of $x$ is $\ldots \ldots \ldots$

Assume there are two identical simple pendulum Clocks$-1$ is placed on the earth and Clock$-2$ is placed on a space station located at a height $h$ above the earth surface. Clock$-1$ and Clock$-2$ operate at time periods $4\,s$ and $6\,s$ respectively. Then the value of $h$ is $....km$ (consider radius of earth $R _{ E }=6400\,km$ and $g$ on earth $10\,m / s ^{2}$ )

If the radius of the earth were to shrink by $1\%$ its mass remaining the same, the acceleration due to gravity on the earth's surface would

If density of a planet is double that of the earth and the radius $1.5$ times that of the earth, the acceleration due to gravity on the surface of the planet is ........

Assuming the earth to be a sphere of uniform density the acceleration due to gravity

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is $..........km$ : [Radius of earth $R =6400 \,km$ and $\sqrt{3}=1.732]$