The radius of planet B is [tex]\sqrt{2[/tex] times the radius of planet A.
Thus it states that bodies with mass attract each other with a force that varies directly as the product of their masses and inversely as the square of the distance between them.
The surface gravity of a planet is given by
g = GM/R²
where
G is the gravitational constant
M is the mass of the planet
R is the radius of the planet
For the two planets in the problem, we have:
gA=gB (same gravity)
MB=2MA (planet B has twice the mass of planet A)
So we can write
GMA/R²A=GMB/R²B
MA/R²A=2MB/R²B
R²B=2R²A
→ RB = √2RA
so, the radius of planet B is √2 times the radius of planet A
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