Acceleration due to gravity is$ ‘g’ $on the surface of the earth. The value of acceleration due to gravity at a height of $32\, km$ above earth’s surface is ........ $g$. (Radius of the earth$ = 6400 \,km$)

If mass of earth decreases by $25 \%$ and its radius increases by $50 \%$, then acceleration due to gravity at its surface decreases by nearly ......... $\%$

A particle of mass $10\, g$ is kept of the surface of a uniform sphere of mass $100\, kg$ and a radius of $10\, cm .$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (you make take $\left.G=6.67 \times 10^{-11} Nm ^{2} / kg ^{2}\right)$

Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of $r$ from the centre is proportional to

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

If a man at the equator would weigh $(3/5)^{th}$ of his weight, the angular speed of the earth is