Question

force on m1 by m2 = 0.000 000 166 852 n
force on m2 by m1 = 0.000 000 166 852 n
how does the force between two objects change
if one object is made ten times more massive?

Explanation:

Step1: Recall Newton's law of universal gravitation

The formula for the gravitational force between two objects is \(F = G\frac{m_1m_2}{r^2}\), where \(G\) is the gravitational constant, \(m_1\) and \(m_2\) are the masses of the two objects, and \(r\) is the distance between their centers of mass.

Step2: Analyze the effect of increasing mass

If one object's mass (\(m_1\) or \(m_2\)) is made ten times more massive (let's say \(m_1'= 10m_1\)), then the new force \(F'=G\frac{(10m_1)m_2}{r^2}\).

Step3: Simplify the new - force expression

Since \(F = G\frac{m_1m_2}{r^2}\), and \(F'=G\frac{(10m_1)m_2}{r^2}\), we can see that \(F' = 10F\).

Answer:

The force between the two objects will be ten times larger.