To solve this problem we will proceed to use the expression of gravity given in Newtonian theory in terms of mass, the radius the universal gravitational constant, that is:
[tex]g = \frac{GM}{R^2}[/tex]
This expression defines as gravity on earth. On another planet with twice the mass and radius constants it would be given as,
[tex]g' = \frac{G2M}{(2R)^2}[/tex]
[tex]g' = \frac{2GM}{4R^2}[/tex]
[tex]g' = \frac{1}{2} *\frac{GM}{R^2}[/tex]
[tex]g' = \frac{g}{2}[/tex]
Expressing the weight of the planet this would be then
[tex]W = mg'[/tex]
[tex]W = m\frac{g}{2}[/tex]
[tex]W = \frac{500N}{2}[/tex]
[tex]W = 250N[/tex]
Correct answer is B.
The weight of person on the new planet is of 250 N. Hence, option (c) is correct.
Given data:
The weight of person on Earth is, W = 500 N.
The standard expression for the weight of person on the new planet is,
W' = mg'
Here, g' is the gravitational acceleration on the new planet.
Let us calculate the gravitational acceleration on the new planet. The standard expression for the gravitational acceleration on the new planet is,
[tex]g'=\dfrac{GM}{R^{2}}[/tex]
Here,
G is the universal gravitational constant.
M is the mass of planet, which is two times the mass of Earth. (M = 2m )
R is the radius of planet, which is twice the radius of Earth. (R = 2r).
Then,
[tex]g'=\dfrac{G \times (2m)}{(2r)^{2}}\\\\g'=\dfrac{2(G \times m)}{4r^{2}}\\\\g'=\dfrac{1}{2} \times \dfrac{(G \times m)}{r^{2}}\\\\g'=\dfrac{1}{2} \times g[/tex]
Here, g is the gravitational acceleration value on Earth. And its value on Earth is [tex]9.8 \;\rm m/s^{2}[/tex].
Then,
[tex]g'=\dfrac{g}{2} \\\\g'=\dfrac{9.8}{2}\\\\g'=4.9 \;\rm m/s^{2}[/tex].
Calculate the mass as,
[tex]W =mg\\500 = m \times 9.8\\m \approx 51 \;\rm kg[/tex]
So weight of person on new planet will be,
[tex]W' = 51 \times 4.9\\W' \approx 250 \;\rm N[/tex]
Thus, we can conclude that the weight of person on the new planet is of 250 N.
Learn more about the gravitational acceleration here:
https://brainly.com/question/3663429
