Choose the correct statement from the following :Weightlessness of an astronaut moving in a satellite is a situation of

The variation of acceleration due to gravity $g$ with distance $d$ from centre of the earth is best represented by ($R =$ Earth's radius)

$Assertion$ : The length of the day is slowly increasing.
$Reason$ : The dominant effect causing a slowdown in the rotation of the earth is the gravitational pull of other planets in the solar system.

Acceleration due to gravity on moon is $\frac 16$ of the acceleration due to gravity on earth. If the ratio of densities of earth $({\rho _e})$ and moon $({\rho _m})$ is $\left( {\frac{{{\rho _e}}}{{{\rho _m}}}} \right) = \frac{5}{3}$ then radius of moon $R_m$ in terms of $R_e$ will be

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 $N\,?$