Question

if the diameter of the earth becomes half of its present value but its average density remains unchanged then how would be the weight of an object on the surface of earth affected.

Answer 1

Let M be the mass of the earth and R be the radius of the earth.
As we know that g = $\frac{GM}{R^2}$
So if the diameter of the earth becomes half, then new radius will become R' = R/2
So g'= $\frac{4GM}{R^2}$= 4g
As we know that W= mg
So new weight W'= mg' = 4mg
i.e., the weight will become 4 times when the diameter of the earth is halved.