Question

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

Answer 1

Weight of an object of mass m,

W = mg = `"G"("Mm")/"R"^2`

When the diameter of the earth becomes half, the radius of the earth also becomes half and mass becomes 4 times its initial value, then

W' = `"G"(4"Mm")/("R"/2)^2`

= `16 "GMm"/"R"^2`

= 16W

i.e., the weight will become 16 times its initial value.