Question

06. A planet has twice the density of earth but the acceleration due to
gravity on its surface is exactly the same as on the surface of earth.
Its radius in terms of radius of earth R will be
a) R/4
b) R/2
c) R/3
d) R/8​

Answer 1

Answer:

b) R/2

Explanation:

g= GM/R²

M= density × volume

= ρ 4/3πR³

g =G ρ 4/3πR³ ÷ R²

g = Gρ 4/3R

∴ g ∝ρ R

ge/gp= Reρe/Rpρp

1 = Reρe/Rpρp (∵ ge = gp given)

Rpρp=  Reρe

Rp × 2ρe = R × ρe(∵  ρp= 2ρe given)

Rp = R/2