Question

Explanation why value of g is zero at the centre of the earth

Answer 1

Why value of g is zero at the centre of earth?

Recall how we determine g :-

We know that force = ma

putting g in place of a, as g is the acceleartion due to gravity.

Also, F = GMm/r²

Where, M is the mass of earth, m is the mass of object, G is gravitational constant and r is the radius of earth.

Equating the two, we get :-

mg = GMm/r²

Cancel m from both sides,

⇒ g = GM/r²

So, the value of g is the mass of earth multiplies with Gravitational constant and divided by the square of the radius of earth.

Now, at the centre of earth, mass would be equal to zero, as all the mass of earth would be above the centre. Hence, substitute M as 0 when it is the centre, :-

g = G × 0/r²

⇒ g = 0

Hence, value of g becomes zero at the centre. This is all because the mass of earth becomes zero at the centre.