Question

1. two spheres have masses of 10 kg and 1.87 kg. if they are placed 0.5 m apart, what is the gravitational force between them?

Explanation:

Step1: Identify the formula

The formula for gravitational force is \(F = G\frac{m_1m_2}{r^2}\), where \(G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}\), \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between them.

Step2: Substitute the values

Given \(m_1 = 10\space kg\), \(m_2=1.87\space kg\), \(r = 0.5\space m\), and \(G = 6.67\times10^{-11}\space Nm^{2}/kg^{2}\).
Substitute into the formula: \(F=6.67\times 10^{-11}\times\frac{10\times1.87}{0.5^{2}}\)
First calculate \(10\times1.87 = 18.7\) and \(0.5^{2}=0.25\)
Then \(\frac{18.7}{0.25}=74.8\)
Now \(F = 6.67\times10^{-11}\times74.8\)
\(F=6.67\times74.8\times10^{-11}\)
\(6.67\times74.8 = 500.916\)
So \(F = 500.916\times10^{-11}\space N\approx5.01\times 10^{-9}\space N\)

Answer:

The gravitational force between them is approximately \(5.01\times 10^{-9}\space N\)