the gravitational force between two objects is 100 n. if the mass of each object is doubled, what is the…

Explanation:

Step1: Recall gravitational - force formula

The gravitational - force formula is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. Initially, $F_1=G\frac{m_1m_2}{r^2}=100\ N$.

Step2: Calculate new force when masses are doubled

When the mass of each object is doubled, $m_1' = 2m_1$ and $m_2' = 2m_2$. The new force $F_2=G\frac{m_1'm_2'}{r^2}=G\frac{(2m_1)(2m_2)}{r^2}=4G\frac{m_1m_2}{r^2}$.

Step3: Substitute initial - force value

Since $G\frac{m_1m_2}{r^2}=F_1 = 100\ N$, then $F_2 = 4F_1$. So $F_2=4\times100\ N = 400\ N$.

Answer:

400 N