Question

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity (presently 9.8m/s²) will be:-
(a)2.45 m/s²
(b)4.9 m/s²
(c)9.8m/s²
(d)19.6m/s²

Answer 1

Explanation:

option D is correct

Acceleration due to gravity g=GM/R² ——-(1)

The radius is constant, volume also constant.

If volume is constant, density is proportional to mass.(v=m/ρ)

The density is doubled, the mass is also doubled. (M’=2M)

The new acceleration due to gravity g’=GM’/R’²

Put the value M’=2M and R’=R

g’=G(2M)/R²

g’=2GM/R² ——–(2)

Substituting equations (1) and (2), we get

g’=2g

g=9.8 m/s²

g’=2×9.8=19.6 m/s²

tq❤