The weight of an object at the centre of the earth of radius $R$ is

Gravitational force on an imaginary planet is six times stronger than the gravitational force of the Earth. Determine the value of acceleration due to gravity and the weight of an object of mass $50 \, kg$ on that planet.

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.

$A$ ball is thrown vertically upwards with a velocity $u$. Calculate the velocity with which it falls to the earth again.

Does the acceleration with which a body falls towards the centre of the earth depend upon its mass?

Choose the correct alternative:
$(a)$ Acceleration due to gravity increases/decreases with increasing altitude.
$(b)$ Acceleration due to gravity increases/decreases with increasing depth.
$(c)$ Acceleration due to gravity is independent of the mass of the earth/mass of the body.