If $R$ is the radius of the Earth and $g$ is the acceleration due to gravity on the Earth's surface,then the mean density of the Earth is:

What should be the angular speed of the Earth so that a body at $60^{\circ}$ latitude becomes weightless? (Radius of Earth $R = 6400 \, km$)

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

If the earth suddenly shrinks (without changing mass) to half of its present radius,the acceleration due to gravity will be

The angular speed of the Earth in $rad/s$,so that bodies on the equator may appear weightless is: [Use $g = 10\, m/s^2$ and the radius of the Earth $R = 6.4 \times 10^3\, km$]

What should be the angular velocity of the Earth due to rotation about its own axis so that the weight of an object at the equator becomes $3/5$ of its initial value? (Radius of Earth at the equator is $R = 6400 \, km$,take $g = 10 \, m/s^2$)