dimension of gravitational constant with proper derivation ?
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The dimensions assigned to the gravitational constant are force times length squared divided by mass squared; this is equivalent to length cubed, divided by mass and by time squared: In SI base units, this amounts to meters cubed per kilogram per second squared: In cgs, G can be written as G ≈ 6.674×10−8 cm3⋅g−1⋅s−2.
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Explanation:
Newtons gravitational law states that the force between two bodies of masses M and m and distance between their centres R is F = GmM/R²
for a body on the surface of earth this force = the weight w
w = mg = GmM/R²
g = GM/R²
G = gR²/M
dimensions of G is L/T²(T²)/M = L/M
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