The dimensions of the universal gravitational | vedclass

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(B) According to Newton's law of universal gravitation,the force $F$ between two masses $m_1$ and $m_2$ separated by a distance $d$ is given by $F = \

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${M^{ - 1}}{L^3}{T^{ - 2}}$

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(B) According to Newton's law of universal gravitation,the force $F$ between two masses $m_1$ and $m_2$ separated by a distance $d$ is given by $F = \frac{G m_1 m_2}{d^2}$.Rearranging the formula to solve for the gravitational constant $G$,we get $G = \frac{F d^2}{m_1 m_2}$.The dimensional formula for force $F$ is $[MLT^{-2}]$,for distance $d$ is $[L]$,and for mass $m$ is $[M]$.Substituting these into the expression for $G$: $[G] = \frac{[MLT^{-2}][L^2]}{[M][M]} = \frac{[ML^3T^{-2}]}{[M^2]} = [M^{-1}L^3T^{-2}]$.

The dimensions of the universal gravitational constant are:

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