What should be the angular speed of the Earth about its axis so that the acceleration due to gravity at the equator becomes zero?

$A$ hole is drilled halfway to the center of the Earth. $A$ body weighs $300 \ N$ on the surface of the Earth. How much will it weigh at the bottom of the hole (in $N$)?

If the density of a planet is double that of the earth and the radius is $1.5$ times that of the earth,the acceleration due to gravity on the surface of the planet is ........

The acceleration due to gravity on the surface of Earth is $g$. If the diameter of Earth reduces to half of its original value and mass remains constant,then the acceleration due to gravity on the surface of Earth would be:

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

$A$ certain planet completes one rotation about its axis in time $T$. The weight of an object placed at the equator on the planet's surface is a fraction $f$ ($f$ is close to unity) of its weight recorded at a latitude of $60^{\circ}$. The density of the planet (assumed to be a uniform perfect sphere) is given by