If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately ........ minutes

(Take : $g =10 \,ms ^{-2},$ the radius of earth, $R =6400 \times 10^{3}\, m ,$ Take $\left.\pi=3.14\right)$

Acceleration due to gravity at surface of a planet is equal to that at surface of earth and density is $1.5$ times that of earth. If radius of earth is $R$, radius of planet is .................

A box weighs $196 \;\mathrm{N}$ on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to ....... $N$

(Take $\mathrm{g}=10\; \mathrm{ms}^{-2}$ at the north pole and the radius of the earth $=6400\; \mathrm{km}$)

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of earth of radius $R$. If $r < R$, then

Find the gravitational field at a distance of $2000\, km$ from centre of earth. (in $m / s ^{2}$)

(Given $\left.R_{\text {earth }}=6400 km , r =2000 km , M _{\text {earth }}=6 \times 10^{24} kg \right)$

An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre of the earth. Where radius of earth, $R=6400\,km$. The percentage decrease in the weight of the object will be $....\%$