Question

current attempt in progress
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?

o 6.9×10^(-10)n
o 9.3×10^(-10)n
o 2.6×10^(-7)n
o 1.5×10^(-7)n
o 6.0×10^(-8)n

Explanation:

Step1: Calculate the distance between the centers

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

Step2: Apply the gravitational - force formula

The gravitational - force formula 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 into the formula:
\[

$$\begin{align*} F&=6.67\times 10^{-11}\frac{65\times87}{2.50^{2}}\\ &=6.67\times 10^{-11}\frac{5655}{6.25}\\ &=6.67\times 10^{-11}\times904.8\\ &\approx6.0\times 10^{-8}\text{ N} \end{align*}$$

\]

Answer:

E. $6.0\times 10^{-8}\text{ N}$