Question

1. according to the law of universal gravitation, what will happen to the gravitational force between two objects when the mass quadruples?

o the gravitational force will increase 2 times
o the gravitational force will increase 4 times
o the gravitational force will increase 16 times
o the gravitational force will increase by 1/4 times

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force 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 them.

Step2: Analyze the effect of quadrupling the mass

Let the original masses be \(m_1\) and \(m_2\), and the new masses be \(4m_1\) and \(4m_2\). The new force \(F'=G\frac{(4m_1)(4m_2)}{r^2}=G\frac{16m_1m_2}{r^2}\).

Step3: Compare the new force with the original force

Since \(F = G\frac{m_1m_2}{r^2}\), we can see that \(F' = 16F\).

Answer:

the gravitational force will increase 16 times