Answer :
Answer:
the radius of planet B is [tex]\sqrt{2}[/tex] times the radius of planet A
Explanation:
The surface gravity of a planet is given by
[tex]g=\frac{GM}{R^2}[/tex]
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:
[tex]g_A = g_B[/tex] (same gravity)
[tex]M_B = 2 M_A[/tex] (planet B has twice the mass of planet A)
So we can write
[tex]\frac{GM_A}{R_A^2}=\frac{GM_B}{R_B^2}\\\frac{M_A}{R_A^2}=\frac{2M_A}{R_B^2}\\R_B^2 = 2R_A^2 \rightarrow R_B = \sqrt{2} R_A[/tex]
so, the radius of planet B is [tex]\sqrt{2}[/tex] times the radius of planet A.