The radius of planet 1 is [tex]\sqrt{3}[/tex] the radius of planet 2.
Explanation:
The gravitational force experienced by a person standing on the surface planet is given by
[tex]F=\frac{GMm}{R^2}[/tex]
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the person
R is the radius of the planet
In this problem, we know that:
Expliciting the two forces, we can write
[tex]F_1 = F_2\\\frac{GM_1 m}{R_1^2}=\frac{GM_2 m}{R_2^2}[/tex]
where [tex]R_1, R_2[/tex] are the radii of the two planets.
Substituting eq.(1) and re-arranging, we find:
[tex]\frac{G(3M_2) m}{R_1^2}=\frac{GM_2 m}{R_2^2}\\R_1^2 = 3R_2^2\\R_1 = \sqrt{3} R_2[/tex]
Which means that the radius of planet 1 is [tex]\sqrt{3}[/tex] the radius of planet 2.
Learn more about gravitational force:
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