Answer:
the distance between the centers of the spheres is 1.72 × 10⁻⁷m
Explanation:
The mass of the two spheres ,m = 99kg
The length of the cable is L= 130.3 m
The gravitational force
[tex]F = \frac{Gm^2}{r^2} = mg\tan\theta[/tex]
[tex]\tan\theta=(\frac{Gm}{gr^2} )[/tex]
Distance change on each side is [tex]L \sin\theta[/tex]
so, the total distance is ,S = [tex]2L\sin\theta[/tex]
For small angle we have,
[tex]\sin\theta=\tan\theta=\theta[/tex]
The above equation can be written as
[tex]S = 2L\sin\theta=2l\theta[/tex]
[tex]S = 2L(\frac{Gm}{gr^2}) \\\\= 2(130.3)(\frac{(6.67\times10^-^1^1)(99)}{(9.8\times1.02)} )\\\\= 1.72\times10^-^7m[/tex]
So, the distance between the centers of the spheres is 1.72 × 10⁻⁷m
