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:

During the motion of a man from the equator to the pole of the Earth,his weight will ....... $\%$ (neglect the effect of change in the radius of the Earth).

The rotation of the earth having radius $R$ about its axis speeds up to a value such that a man at latitude angle $60^{\circ}$ feels weightless. The duration of the day in such case will be:

The weight of a body of mass $m$ decreases by $1\%$ when it is taken to a height $h$ above the surface of the Earth. What is the percentage decrease in its weight when it is taken to a depth $h$ below the surface of the Earth?

The period of oscillation of a simple pendulum of constant length at the Earth's surface is $T$. Its period inside a mine is

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