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 is directly proportional to the mass of the earth and inversely proportional to the square of the radius of the earth. i.e.

Weight of a body ∝ M/ R²

Original weight W_o = m g = m G (M /R²)

When hypothetically M becomes 4 M and R becomes R /2

then weight becomes W_n= m G (4M/ (R/2)² = (16 m G) M /R² = 16 × W_o

The weight will become 16 times.