At what height over the earth's pole, the free fall acceleration decreases by one percent ........ $km$. (assume the radius of earth to be $6400 \,km$)

If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2 \mathrm{~m} / \mathrm{s}^2$, then the length of the second's pendulum at a height $h=2 R$ from the surface of earth will be,:

If the earth stops rotating, the value of $‘g’$ at the equator will

A pendulum clock is set to give correct time at the sea level. This clock is moved to hill station at an altitude of $2500\, m$ above the sea level. In order to keep correct time of the hill station, the length of the pendulum

If the radius of earth shrinks by $2 \%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately.

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 $N\,?$