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
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
(1)
where M is the Earth's mass and R is the Earth's radius.
For the unknown planet, we have:
(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)
(the mass of the planet is half the mass of the Earth)
Therefore, eq.(2) becomes
(3)
By dividing eq.(1) by eq.(3), we get
So, the radius of the planet is half that of Earth.
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