Question

the gravitational force between two objects is 100 n. if the mass of each object is doubled, what is the gravitational force between the objects at the same distance? 25 n 50 n 200 n 400 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. Initially, $F_1=G\frac{m_1m_2}{r^2}=100$ N.

Step2: Calculate the 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 $F_2=G\frac{m_1'm_2'}{r^2}=G\frac{(2m_1)(2m_2)}{r^2}=4G\frac{m_1m_2}{r^2}$.
Since $G\frac{m_1m_2}{r^2}=F_1 = 100$ N, then $F_2 = 4\times100$ N.

Answer:

400 N