The radii of two planets $A$ and $B$ are $R$ and $4R$ and their densities are $\rho$ and $\rho/3$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_A : g_B)$ will be

If the value of $g$ (acceleration due to gravity) at the Earth's surface is $10 \ m/s^2$,what is its value in $m/s^2$ at the center of the Earth,assuming the Earth is a sphere of radius $R$ meters with uniform mass density?

If all objects on the equator of the earth feel weightless,then the duration of the day will nearly become ....... $hr$.

Suppose that the force of earth's gravity suddenly disappears,choose the correct answer out of the following statements.

Which graph correctly represents the variation of acceleration due to gravity $(g)$ with radial distance $(r)$ from the centre of the earth (radius of the earth $= R_e$)?

The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If $R$ is the radius of earth,then the radius of the planet would be