Question

How does the weight of an object vary with respect to the mass and the radius of the earth? 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

Answer:

The weight of the body will be 16 times the original weight.

Explanation:

As we know, weight of any object = mass * gravitational acceleration

gravitational acceleration = GM/$R^{2}$, where G is universal gravitation constant, M is the mass of the planet, and R is the radius of the planet. Hence if the mass of the planet becomes four times and diameter i.e. radius of planet is halved, then the value of gravitational acceleration will be 16 times the original. Hence the weight of the body will also be 16 times the original weight if we do the following change.