Question

The weight of an object at the centre of the earth of radius R is :
(a) zero
(b) R times the weight at the surface of the earth
(c) infinite
(d) $1/R^2$times the weight at the surface of the earth

Answer 1

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

The weight of an object is the maximum at the surface of the earth. As you move the body closer to the center of the earth, the mass of the earth between the center of the earth and the body keeps decreasing. This causes the force acting from the center of the earth on the body to decrease.