Question

the gravitational force between two objects is 45,000 n. what will be the gravitational force between the two objects if the distance between the objects is reduced by one - half?
11,250 n
22,500 n
90,000 n
180,000 n

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 $F_1 = G\frac{m_1m_2}{r_1^2}=45000$ N.

Step2: Analyze the new - distance case

When the distance is reduced by one - half, $r_2=\frac{1}{2}r_1$. The new force $F_2 = G\frac{m_1m_2}{r_2^2}=G\frac{m_1m_2}{(\frac{1}{2}r_1)^2}$.

Step3: Simplify the new - force expression

$F_2 = G\frac{m_1m_2}{\frac{1}{4}r_1^2}=4\times G\frac{m_1m_2}{r_1^2}$. Since $F_1 = G\frac{m_1m_2}{r_1^2}=45000$ N, then $F_2 = 4F_1$.

Step4: Calculate the new force

$F_2=4\times45000 = 180000$ N.

Answer:

D. 180,000 N