Question

If the diameter of the earth becomes half its present value but its average density remains unchanged then how would be the weight of an object on the surface of the earth affected?

(a) The weight of the object remains unchanged

(b) The weight is doubled

(c) The weight will become one-fourth of the present value

(d) The weight is halved

I got this question in an interview.

Question is taken from Gravitational Potential Field topic in chapter Mechanical Properties of Solids of Engineering Physics I

Answer 1

Correct answer is (d) The weight is halved

The explanation: Acceleration due to gravity on the surface of the earth

g=GM/R^2 = G/R^2 ×4/3 πR^3 ρ=4/3 πGRρ

When the diameter or radius becomes half its present value,

g^‘=4/3 πG R/2 ρ=g/2

Hence the weight of the object will be halved.