When a body is taken from the equator to the poles, its weight

Assuming the earth to be a sphere of uniform mass density, a body weighed $300 \mathrm{~N}$ on the surface of earth. How much it would weigh at $R / 4$ depth under surface of earth?

A space station consists of two living modules attached to a central hub on opposite sides of the hub by long corridors of equal length. Each living module contains $N$ astronauts of  equal mass. The mass of the space station is negligible compared to the mass of the astronauts, and the size of the central hub and living modules is negligible compared to the length of the corridors. At the beginning of the day, the space station is rotating so that the astronauts feel as if they are in gravitational field of strength $g.$ Two astronauts, one from each module, climb into the central hub, and the remaining astronauts now feel a gravitational of strength $g'.$ What is the ratio $g'/g$ in terms of $N\,?$

A body weighs $144 \,N$ at the surface of earth. When it is taken to a height of $h=3 \,R$, where $R$ is radius of earth, it would weigh .......... $N$

If the radius of the earth be increased by a factor of $5,$ by what factor its density be changed to keep the value of $g$ the same ?

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be........ $m/{s^2}$ . $(g = 9.8\,m/{s^2})$