The planet radius is R/2 (half of the Earth's radius)
Explanation:
The strength of the gravitational field at the surface 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 Earth, we can write the strength of the gravitational field at the surface as
[tex]g=\frac{GM}{R^2}[/tex] (1)
where M is the Earth's mass and R is the Earth's radius.
For the unknown planet, we have:
[tex]g'=\frac{GM'}{R'^2}[/tex] (2)
where M' is the mass of the planet and R' its radius.
We know the following:
g' = 2g (the strength of the gravitational field is twice that of Earth)
[tex]M' = \frac{M}{2}[/tex] (the mass of the planet is half the mass of the Earth)
Therefore, eq.(2) becomes
[tex]2g = \frac{G(M/2)}{R'^2}[/tex] (3)
By dividing eq.(1) by eq.(3), we get
[tex]\frac{1}{2}=\frac{2R'^2}{R^2}\\R'^2 = \frac{1}{4}R^2\\R'=\frac{R}{2}[/tex]
So, the radius of the planet is half that of Earth.
Learn more about gravitational force:
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