Dimensional formula for the universal gravita | vedclass

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(A) According to Newton's law of gravitation,the force $F$ between two masses $M_1$ and $M_2$ separated by a distance $R$ is given by: $F = \frac{G M_

Vedclass · Accepted Answer

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

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(A) According to Newton's law of gravitation,the force $F$ between two masses $M_1$ and $M_2$ separated by a distance $R$ is given by: $F = \frac{G M_1 M_2}{R^2}$ Rearranging the formula to solve for the universal gravitational constant $G$: $G = \frac{F R^2}{M_1 M_2}$ Substituting the dimensional formulas for force $[F] = [MLT^{-2}]$,distance $[R] = [L]$,and mass $[M] = [M]$: $[G] = \frac{[MLT^{-2}] [L^2]}{[M] [M]} = \frac{[ML^3 T^{-2}]}{[M^2]} = [M^{-1} L^3 T^{-2}]$

Dimensional formula for the universal gravitational constant is

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