At what height over the earth's pole,the free fall acceleration decreases by one percent? (Assume the radius of earth to be $6400 \, km$)

The value of acceleration due to gravity at a height of $10 \,km$ from the surface of the Earth is $x$. At what depth inside the Earth is the value of the acceleration due to gravity the same value $x$ (in $\,km$)?

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 $= 9.8\, m/s^2$)

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to the Earth's rotation.

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?

$Assertion$ : In a free fall,weight of a body becomes effectively zero.
$Reason$ : Acceleration due to gravity acting on a body having free fall is zero.