If earth is supposed to be a sphere of radius R, if $g_{30}$ is value of acceleration due to gravity at latitude of $ 30^\circ$ and g at the equator, the value of $g – {g_{{{30}^o}}}$ is

A body weights $49\,N$ on a spring balance at the north pole. ….. $N$ will be its weight recorded on the same weighing machine, if it is shifted to the equator?

(Use $g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}$ and radius of earth, $R =6400\, km .]$

The weight of an astronaut, in an artificial satellite revolving around the earth, is

If acceleration due to gravity at distance $d[ < R]$ from the centre of earth is $\beta$, then its value at distance $d$ above the surface of earth will be [where $R$ is radius of earth]

There is no atmosphere on the moon because