Answer :
Answer:
[tex]g=16.28m/s^2[/tex]
Explanation:
The gravitational acceleration on the surface of the earth is
[tex]g_{e}=\frac{Gm_{e}}{R_{e}^2}[/tex]
where G is the universal gravitational constant, [tex]m_{e}[/tex] is the mass of earth, and [tex]R_{e}[/tex] is the radius of earth,
in general for any object the gravitational acceleration or gravity on its surface is:
[tex]g=\frac{Gm}{R^{2}}[/tex]
in this case we know that the mass is 1.66 times the mass of earth:
[tex]m=1.66*m_{e}[/tex]
and the radius is the same as for earth:
[tex]R=R_{e}[/tex]
so the gravity for this planet is
[tex]g=\frac{G(1.66m_{e})}{R_{e}^2}[/tex]
which can be written in the following form:
[tex]g=(1.66)\frac{Gm_{e}}{R_{e}^2}[/tex]
where we know that [tex]g_{e}=\frac{Gm_{e}}{R_{e}^2}[/tex] , so:
[tex]g=(1.66)g_{e}[/tex]
and the acceleration of gravity on earth is: [tex]g_{e}=9.81m/s^2[/tex]
so the acceleration or gravity on the planet is:
[tex]g=(1.66)(9.81m/s^2)\\g=16.28m/s^2[/tex]