Physics

On dividing  dimension of gravitational constant by the dimension of surface tension we get


ANSWER

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


SOLUTION
By Newton's law of gravitation, $$F=\dfrac{Gm_1m_2}{r^2}$$ or $$G=\dfrac{Fr^2}{m_1m_2}$$
So, $$[G]=\dfrac{[MLT^{-2}][L^2]}{[M][M]}=[M^{-1}L^3T^{-2}]$$

Surface tension $$=$$ force/length or $$S=F/l$$
So, $$[S]=\dfrac{[MLT^{-2}]}{[L]}=[MT^{-2}]$$

Thus, $$\dfrac{[G]}{[S]}=\dfrac{[M^{-1}L^3T^{-2}]}{[MT^{-2}]}=[M^{-2}L^3]$$
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Single Correct Medium Published on 18th 08, 2020
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