What is the weight of a body at the centre of the Earth and why?

Weight of a body is the force with which it is attracted towards the centre of earth.

The weight of a body,‘w’ of mass ‘m’ is given by: W =mg

where ‘g’ is the acceleration due to gravity

At the centre of earth, value of g is zero.

Therefore:

Weight of a body at the centre of the earth, w = mg

At the centre of earth, g=0

Weight=m × 0

Weight =0

As the acceleration due to gravity is zero at the centre of earth, weight of a body is zero at the centre of earth.