The acceleration due to gravity about the earth's surface would be half of its value on the surface of the earth at an altitude of ......... $mile$. ($R = 4000$ mile)

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in $N$) half way down to the centre of the earth if it weighed $250\; N$ on the surface?

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.

Reason $R $: At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

Given below are two statements:

Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement $II:$ Acceleration due to earth's gravity is same at a height ' $h$ ' and depth ' $d$ ' from earth's surface, if $h = d$.

In the light of above statements, choose the most appropriate answer form the options given below

Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above  the Earth's surface. If the body is taken to a depth $h$ in a mine, then its weight will

At what altitude in metre will the acceleration due to gravity be $25\%$ of that at the earth's surface (Radius of earth $= R\, metre$)