Question

What is the weight of the body at the centre of the earth ? With support your answer explain

Answer 1

zero. when in center, all the mass of earth which is surrounding the object will attract it towards itself thus all the forces will nullify each other.
gravitational force exerted by a body is the vector sum of all the forces exerted by its particles , now because all the mass of earth will be surrounding the object in center , their forces which are equal in magnitude in all directions but of course opposite to each other, will cancel out each other.