Answer:
c. Jupiter's radius is 10 times the Earth's radius
Explanation:
The weight of a person on the surface of a planet is equal to the gravitational pull exerted by the planet on the person:
![F=G\frac{mM}{R^2}](https://tex.z-dn.net/?f=F%3DG%5Cfrac%7BmM%7D%7BR%5E2%7D)
where
is the gravitational constant
M is the mass of the planet
m is the mass of the person
R is the radius of the planet
The weight of a person on Earth is given by:
![F_E=G\frac{mM_E}{R_E^2}](https://tex.z-dn.net/?f=F_E%3DG%5Cfrac%7BmM_E%7D%7BR_E%5E2%7D)
where
is the mass of the Earth and
is the Earth's radius.
We know that Jupiter's mass is 300 times the Earth's mass:
![M_J = 300 M_E](https://tex.z-dn.net/?f=M_J%20%3D%20300%20M_E)
while Jupiter's radius is 10 times the Earth's radius:
![R_J = 10 R_E](https://tex.z-dn.net/?f=R_J%20%3D%2010%20R_E)
So, the weight of the person on Jupiter is
![F_J=G\frac{mM_J}{R_J^2}=G\frac{m(300 M_E)}{(10 R_E)^2}=G \frac{300 mM_E}{100 R_E^2}=3 G\frac{mM_E}{R_E^2}=3 F_E](https://tex.z-dn.net/?f=F_J%3DG%5Cfrac%7BmM_J%7D%7BR_J%5E2%7D%3DG%5Cfrac%7Bm%28300%20M_E%29%7D%7B%2810%20R_E%29%5E2%7D%3DG%20%5Cfrac%7B300%20mM_E%7D%7B100%20R_E%5E2%7D%3D3%20G%5Cfrac%7BmM_E%7D%7BR_E%5E2%7D%3D3%20F_E)
So, the weight would be only 3 times as much.