$A$ body weighs $63 \; N$ on the surface of the earth. What is the gravitational force (in $N$) on it due to the earth at a height equal to half the radius of the earth?

The acceleration due to gravity at height $h$ above the earth if $h \ll R$ (radius of earth) is given by

The percentage decrease in the weight of a rocket,when taken to a height of $32 \ km$ above the surface of the Earth,will be $.....\%$
(Radius of Earth $= 6400 \ km$)

State whether the following statements are true or false:
$(a)$ $G$ is a vector quantity.
$(b)$ The relation $g = \frac{GM}{r^2}$ holds well for all celestial bodies.
$(c)$ If the Earth suddenly stops rotating,the value of acceleration due to gravity at the equator will decrease.

Consider Earth to be a homogeneous sphere. Scientist $A$ goes deep down in a mine and scientist $B$ goes high up in a balloon. The value of $g$ measured by

The radius of the Earth is approximately $6000 \, km$. The weight of a body at a height of $6000 \, km$ from the Earth's surface becomes: