Question

What must be the units for the gravitational constant G in order for gravitational force to have units of newtons?

Answer 1

Answer:

m³/(kg⋅s²)

Explanation:

Hello.

In this case, since the involved formula is:

$F=G*\frac{m_1m_2}{r^2}$

By writing a dimensional analysis with the proper algebra handling, we obtain:

$N[=]G*\frac{kg*kg}{m^2}\\ \\kg*\frac{m}{s^2}[=]G *\frac{kg*kg}{m^2}\\\\G[=]\frac{kg*m*m^2}{kg^2*s^2}\\ \\G[=]\frac{m^3}{kg*s^2}$

Thus, answer is:

m³/(kg⋅s²)

Note that the [=] is used to indicate the units of G.

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