Answer:
The weight at a distance 2R from the surface of Earth will be [tex]F'=10 N[/tex].
Explanation:
First of all, we need to find the acceleration of gravity at 2R. Using the gravitational force equation
[tex]F=G\frac{mM}{R^{2}}[/tex]
Where:
M is the mass of the earth
m is the mass of the object
G is the gravitational constant
R is the radius of the earth
We can equal the gravitational force with the second Newton's law (F=ma)
[tex]F=G\frac{mM}{R^{2}}[/tex]
[tex]mg=G\frac{mM}{R^{2}}[/tex]
We know the weight at the earth surface is 90 N, which means:
[tex]90=G\frac{mM}{R^{2}}[/tex]
Now, we have the same equation in the case of 2R as a distance from the surface of the object. Let's remember we need to use the distance from the center of the mass of the earth, so in this case, will be 3R.
[tex]F'=G\frac{mM}{(3R)^{2}}[/tex]
[tex]F'=G\frac{mM}{9R^{2}}[/tex]
[tex]F'=\frac{1}{9}G\frac{mM}{R^{2}}[/tex]
Using the above equation we have:
[tex]F'=\frac{1}{9}90[/tex]
[tex]F'=\frac{90}{9}[/tex]
Therefore, the weight at a distance 2R from the surface of Earth will be [tex]F'=10 N[/tex].
I hope it helps you!
