the gravitational force between two objects is 1600 n. what will be the gravitational force between 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. Let the initial force be $F_1 = G\frac{m_1m_2}{r_1^2}=1600$ N.

Step2: Analyze the new - distance situation

When the distance doubles, $r_2 = 2r_1$. The new force $F_2=G\frac{m_1m_2}{r_2^2}=G\frac{m_1m_2}{(2r_1)^2}$.

Step3: Express $F_2$ in terms of $F_1$

$F_2=G\frac{m_1m_2}{4r_1^2}=\frac{1}{4}\times G\frac{m_1m_2}{r_1^2}$. Since $F_1 = G\frac{m_1m_2}{r_1^2}=1600$ N, then $F_2=\frac{F_1}{4}$.

Step4: Calculate $F_2$

$F_2=\frac{1600}{4}=400$ N.

Answer:

A. 400 N