Question

what happens to the force of attraction between two planets when the masses of both are doubled? view available hint(s) hint 1. let the equation for gravity guide your thinking. the force quadruples. the force doubles. the force remains the same. the force increases by 16.

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula between two objects with masses $m_1$ and $m_2$ separated by a distance $r$ is $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant.

Step2: Double the masses

Let the new masses be $m_1' = 2m_1$ and $m_2' = 2m_2$. The new force $F'$ is $F'=G\frac{m_1'm_2'}{r^2}=G\frac{(2m_1)(2m_2)}{r^2}$.

Step3: Simplify the new - force expression

$F' = G\frac{4m_1m_2}{r^2}=4\times G\frac{m_1m_2}{r^2}=4F$.

Answer:

The force quadruples.