Question

1. the force of gravitational attraction between two objects, each of mass m, is given by the formula ( f = \frac{gm^2}{r^2} ), where f is the force of attraction, g is a constant, and r is the distance between the objects. which of the following expresses g in terms of f, m, and r? ( \bigcirc g = \frac{fr^2}{m^2} ) ( \bigcirc g = \frac{r^2}{fm^2} ) ( \bigcirc g = \frac{fm^2}{r^2} ) ( \bigcirc g = \frac{m^2}{fr^2} )

Explanation:

Step1: Start with the given formula

We have the formula for gravitational force: \( F = \frac{Gm^2}{r^2} \). Our goal is to solve for \( G \) in terms of \( F \), \( m \), and \( r \).

Step2: Multiply both sides by \( r^2 \)

To isolate the term with \( G \), we multiply both sides of the equation by \( r^2 \). This gives us:
\( F \times r^2 = \frac{Gm^2}{r^2} \times r^2 \)
Simplifying the right - hand side, the \( r^2 \) in the numerator and denominator cancels out, so we have \( Fr^2=Gm^2 \).

Step3: Divide both sides by \( m^2 \)

Now, to solve for \( G \), we divide both sides of the equation \( Fr^2 = Gm^2 \) by \( m^2 \). So:
\( G=\frac{Fr^2}{m^2} \)

Answer:

\( G = \frac{Fr^2}{m^2} \) (corresponding to the first option)