What is the dimension of gravitational constant?

ML³T⁻²

M⁻¹L³T⁻²

M²L⁻²T⁻²

M²L⁻¹T⁻²

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UPSC NDA-1 – 2022

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The dimension of the gravitational constant ($G$) is M⁻¹L³T⁻².

The gravitational constant $G$ appears in Newton’s Law of Universal Gravitation, which states that the force ($F$) between two masses ($m_1$, $m_2$) separated by a distance ($r$) is given by $F = G \frac{m_1 m_2}{r^2}$.

We can determine the dimensions of $G$ by rearranging the formula: $G = \frac{F r^2}{m_1 m_2}$. The dimensions of Force ($F$) are [MLT⁻²], distance ($r$) are [L], and mass ($m$) are [M]. Substituting these dimensions: $[G] = \frac{[MLT⁻²] [L]^2}{[M][M]} = \frac{[ML³T⁻²]}{[M²]} = [M^{1-2} L³ T⁻²] = [M⁻¹L³T⁻²]$.

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