Question

How does the weight of an object vary with respect to its mass and radius earth. in a hypothetical case if the diameter of the earth becomes half of its present value and mass become four time its present value then how would weight of any object on surface of earth is affected?

Answer 1

weight of an object=mass of the object × gravity of earth

mass of earth remains same everywhere

gravity is given by

g=GMm/R²

M=mass of earth

m=mass of object

R=radius of earth

G=universal gravitational constant

g=9.8m/s² on earth

so if the diameter of the earth becomes half of its present value and mass become four time its present value then.

R'=R/2 and M'=4M

g'=GM'm/R'²

g'=G(4M)m/(R/2)²

g'=16GMm/R²

g'=16g

so the weight of the body will be

mass×g' =mass×16g=16 times the initial weight