The value of the gravity acceleration on the planet's surface increases
Explanation:
The gravitational acceleration on 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
In this problem, we are told that the planet shrinks, therefore the new radius is smaller than the original radius:
[tex]R'<R[/tex]
while the mass remains the same:
[tex]M'=M[/tex]
Therefore, the new acceleration of gravity is
[tex]g'=\frac{GM}{R'^2}[/tex]
We see that the value of g is inversely proportional to the square of the radius of the planet: therefore, since [tex]R'<R[/tex], it means that [tex]g'>g[/tex], so when the planet shrinks, the value of the gravity acceleration on the planet's surface increases.
Learn more about gravity:
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