Question

what must be the units for the gravitational constant g in order for gravitational force to have units of newtons? (1 point)

\\( \frac { n \cdot m ^ { 2 } } { k g ^ { 2 } } \\)

\\( \frac { n \cdot m ^ { 3 } } { k g ^ { 3 } } \\)

\\( \frac { n \cdot m } { k g ^ { 2 } } \\)

\\( \frac { n \cdot m } { k g } \\)

Explanation:

Step1: Recall Newton's law of gravitation formula

Newton's law of gravitation is \(F = G\frac{m_1m_2}{r^2}\), where \(F\) is the gravitational force, \(m_1\) and \(m_2\) are masses, \(r\) is the distance between the masses, and \(G\) is the gravitational constant.

Step2: Solve for \(G\) in terms of units

We can rewrite the formula for \(G\) as \(G=\frac{F r^{2}}{m_1m_2}\).
The unit of \(F\) is \(N\) (newton), the unit of \(r\) is \(m\) (meter), and the unit of \(m\) (mass) is \(kg\) (kilogram).
Substituting the units: \(G\) has units \(\frac{N\cdot m^{2}}{kg\cdot kg}=\frac{N\cdot m^{2}}{kg^{2}}\)

Answer:

\(\frac{N\cdot m^{2}}{kg^{2}}\) (first option)