The height of any point $P$ above the surface of the Earth is equal to the diameter of the Earth. The value of acceleration due to gravity at point $P$ will be: (Given $g = $ acceleration due to gravity at the surface of the Earth)

Consider Earth to be a sphere of radius $R_e$ rotating about its own axis with angular speed $\omega$. If $g_{E}$ and $g_{P}$ are the accelerations due to gravity at the equator and the poles respectively,then $(g_{P}-g_{E})$ is given by $\left[\cos (0^{\circ})=\sin (\frac{\pi}{2})=1, \sin (0^{\circ})=\cos (\frac{\pi}{2})=0\right]$

Two planets $A$ and $B$ of radii $R$ and $1.5 R$ have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to $A$ is:

At what altitude will the acceleration due to gravity be $25\%$ of that at the earth's surface (given radius of earth is $R$)?

Which of the following statements are true about acceleration due to gravity?
$(a)$ '$g$' decreases in moving away from the centre if $r > R$
$(b)$ '$g$' decreases in moving towards the centre if $r < R$
$(c)$ '$g$' is zero at the centre of the Earth
$(d)$ '$g$' decreases if the Earth stops rotating on its axis

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is