Question

one uniform sphere of matter has a radius of 0.50 m and a mass of 65 kg. a second uniform sphere has a radius of 0.80 m and a mass of 87 kg. the surfaces of the spheres are 1.20 m apart, as measured on a line drawn between the centers of the spheres. what is the magnitude of the gravitational force that each sphere exerts on the other? 6.9×10^(-10)n 9.3×10^(-10)n 2.6×10^(-7)n 1.5×10^(-7)n 6.0×10^(-8)n

Explanation:

Step1: Calculate the distance between centers

The distance between the centers of the spheres $r$ is the sum of the two radii and the distance between the surfaces. So $r=0.50 + 1.20+0.80=2.50$ m.

Step2: Apply Newton's law of gravitation

Newton's law of gravitation is $F = G\frac{m_1m_2}{r^2}$, where $G = 6.67\times10^{- 11}\text{ N}\cdot\text{m}^2/\text{kg}^2$, $m_1 = 65$ kg, $m_2=87$ kg and $r = 2.50$ m.
Substitute the values: $F=6.67\times 10^{-11}\times\frac{65\times87}{2.50^{2}}$.
First, calculate $65\times87 = 5655$.
Then, $2.50^{2}=6.25$.
So $F=6.67\times 10^{-11}\times\frac{5655}{6.25}$.
$\frac{5655}{6.25}=904.8$.
$F=6.67\times10^{-11}\times904.8\approx6.0\times 10^{-8}$ N.

Answer:

$6.0\times 10^{-8}$ N