In Newton's Law of Gravity the universal gravitational constant G = Fr²/m₁m₂,where F is the gravitational force between the two masses,m₁ and m₂,and r is the distance between them.What are the dimensions of G? A)L²M^-1T ² B)L³M^-1T ^-2 C)L²M^-2T ^-2 D)L³M^-1T ² E)L^-3M¹T ³

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Quizplus · Accepted Answer

The dimensions of G can be derived from the formula $G = \frac{F r^2}{m_1 m_2}$, where $F$ is the force (with dimensions $MLT^{-2}$), $r$ is the distance (with dimensions $L$), and $m_1$ and $m_2$ are masses (each with dimensions $M$). Rearranging for $G$, we get dimensions $L^3M^{-1}T^{-2}$, which matches choice B.

In Newton's Law of Gravity the Universal Gravitational Constant G