The gravitational field strength on Planet X is approximately [tex]7.36 m/s^2[/tex]
Explanation:
The gravitational field strength 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
On the Earth's surface,
[tex]g_E = \frac{GM_E}{R_E^2}=9.81 m/s^2[/tex]
where [tex]M_E[/tex] is the Earth's mass and [tex]R_E[/tex] is the Earth's radius.
Planet X has:
- Mass three times the Earth's mass: [tex]M_X = 3M_E[/tex]
- Radius twice the Earth's radius: [tex]R_X =2R_E[/tex]
So its gravitational field strength is
[tex]g_X = \frac{GM_X}{R_X^2}=\frac{G(3M_E)}{(2R_E)^2}=\frac{3}{4}(\frac{GM_E}{R_E^2})=\frac{3}{4}g_E = \frac{3}{4}(9.81)=7.36 m/s^2[/tex]
Learn more about gravitational force:
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