Question

the weight of the particle at the centre of the earth is​

Answer 1

the weight of the particle at the centre of the earth is 0

Answer 2

Explanation:

The closer to the center, the more is pulling away, until right at the center the entire Earth is pulling the object away from the center. The sum of all these pulls makes the weight of a particle at the center zero (there's Calculus to show that in this case, (G 0 M2) / 0^2 is zero, not anything else).