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

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:

The weight of a body at the centre of the earth is

Which of the following statements are true about the acceleration due to gravity of the Earth (where $r$ is the distance from the center of the Earth and $R$ is the radius of the Earth)?
$(a)$ $g$ decreases when moving away from the center, if $r > R$.
$(b)$ $g$ decreases when moving away from the center, if $r < R$.
$(c)$ $g$ is zero at the center of the Earth.
$(d)$ $g$ at the equator decreases, if the Earth stops rotating about its axis.

The acceleration due to gravity becomes $\left(\frac{g}{2}\right)$ ($g =$ acceleration due to gravity on the surface of the earth) at a height equal to

Let $g$ be the acceleration due to gravity at the Earth's surface and $K$ be the rotational kinetic energy of the Earth. Suppose the Earth's radius decreases by $2 \%$ keeping its mass the same,then: