Question

If the diameter if the earth becomes twice its present value but its mass remains unchanged, then how would be the weight of an object on the surface of the earth affected?

(a) 1/2 W

(b) 1/3 W

(c) 1/4 W

(d) W

This question was posed to me during an online interview.

My question is based upon Intensity of Gravitational Field topic in section Mechanical Properties of Solids of Engineering Physics I

Answer 1

The correct choice is (c) 1/4 W

For explanation I would say: Weight of the body,

W=mg=GMm/R^2

When the diameter or radius of the earth becomes double its present value, the weight of the body will be

W’=GMm/((2R)^2 )=1/4 W

That is, the weight will become one-fourth of the present value.