select the correct answer.\nobject a attracts object b with a gravitational force of 5 newtons from a given…

Explanation:

Step1: Recall gravitational - force formula

The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^2}$, 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. Let the initial force be $F_1 = G\frac{m_1m_2}{r_1^2}=5$ N.

Step2: Analyze the new - distance situation

The new distance $r_2=\frac{r_1}{2}$. The new force $F_2 = G\frac{m_1m_2}{r_2^2}=G\frac{m_1m_2}{(\frac{r_1}{2})^2}=G\frac{m_1m_2}{\frac{r_1^2}{4}} = 4\times G\frac{m_1m_2}{r_1^2}$.

Step3: Calculate the new force

Since $F_1 = G\frac{m_1m_2}{r_1^2}=5$ N, then $F_2 = 4F_1$. Substituting $F_1 = 5$ N, we get $F_2=4\times5 = 20$ N.

Answer:

D. 20 newtons