If the density of earth is doubled keeping its radius constant then acceleration

If the density of earth is doubled keeping its radius constant then acceleration due to gravity will be (g=9.8 m/s²)

Options

(a) 19.6 m/s²
(b) 9.8 m/s²
(c) 4.9 m/s²
(d) 2.45 m/s²

Correct Answer:

19.6 m/s²

Explanation:

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

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