Question

the gravitational force formula is \\(f = \frac{g m_1 m_2}{r^2}\\), where \\(f\\) is the force between two objects, \\(g\\) is the constant of gravitation, \\(m_1\\) is the mass of the first object, \\(m_2\\) is the mass of the second object, and \\(r\\) is the distance between the objects. by rewriting the formula as \\(r = \sqrt{\frac{g m_1 m_2}{f}}\\), you can find the distance between objects. which of the following gives the distance, \\(r\\), in simplest form?

\\(r = \frac{\sqrt{g m_1 m_2}}{f}\\)

\\(r = \frac{\sqrt{g m_1 m_2 f}}{f}\\)

\\(r = \sqrt{g m_1 m_2 f}\\)

Explanation:

Apply the quotient property of radicals

Using the Quotient Property of Radicals knowledge point

$$ r = \sqrt{\frac{G m_1 m_2}{F}} = \frac{\sqrt{G m_1 m_2}}{\sqrt{F}} $$

Rationalize the denominator

Using the Rationalizing the Denominator knowledge point

$$ r = \frac{\sqrt{G m_1 m_2} \cdot \sqrt{F}}{\sqrt{F} \cdot \sqrt{F}} = \frac{\sqrt{G m_1 m_2 F}}{F} $$

Answer:

• (A) \(r = \frac{\sqrt{G m_1 m_2}}{F}\)
• (B) \(r = \frac{\sqrt{G m_1 m_2 F}}{F}\) (Correct answer)
• (C) \(r = \sqrt{G m_1 m_2 F}\)