The value of the acceleration due to gravity is $g_{1}$ at a height $h = \frac{R}{2}$ ($R$ = radius of the earth) from the surface of the earth. It is again equal to $g_{1}$ at a depth $d$ below the surface of the earth. The ratio $\left(\frac{d}{R}\right)$ equals

Weight of a body decreases by $1.5 \%$ when it is raised to a height $h$ above the surface of the Earth. When the same body is taken to the same depth $h$ in a mine,its weight will show ........

Which of the following statements are true about the acceleration due to gravity of the Earth (where $r$ is the distance from the center of the Earth and $R$ is the radius of the Earth)?
$(a)$ $g$ decreases when moving away from the center, if $r > R$.
$(b)$ $g$ decreases when moving away from the center, if $r < R$.
$(c)$ $g$ is zero at the center of the Earth.
$(d)$ $g$ at the equator decreases, if the Earth stops rotating about its axis.

The angular speed of the Earth in $rad/s$,so that bodies on the equator may appear weightless is: [Use $g = 10\, m/s^2$ and the radius of the Earth $R = 6.4 \times 10^3\, km$]

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ $A$ pendulum clock when taken to Mount Everest becomes fast.
Reason $R:$ The value of $g$ (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.
In the light of the above statements,choose the most appropriate answer from the options given below.

The average density of the Earth is [ $g$ is acceleration due to gravity]: