# Derive the Dimensional Formula of Universal Constant of Gravitation?

Posted in Dimensional Formulae | Email This Post |Universal Constant of Gravitation is represented by G and is derived from Newton’s law of gravitation. Newton’s law states that

F=(Gm_{1}m_{2})/r^{2}

So

G=(Fr^{2})/m_{1}m_{2}

Where F is Force between masses m_{1}, m_{2} at a distance r

Dimensional Formula of Force= M^{1}L^{1}T^{-2}

Thus

Dimensional Formula of Universal Constant of Gravitation= (M^{1}L^{1}T^{-2} x L^{2})/(M^{1 }x M^{1})

**Dimensional Formula of Universal Constant of Gravitation = M ^{-1}L^{3}T^{-2}**

SI unit of Universal Constant of Gravitation is Nm^{2}kg^{-2}

or

**Dimensional Formula of Gravitational constant = M ^{-1}L^{3}T^{-2}**

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I didn’t understand that how M-1 came in the answer

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look M1 L1 T-2 x L2 IS THE NUMERATOR

M 1 M 1 IS THE DENOMINATOR

SO M1 and M1 GETS CANCEL and ANOTHER M1 GOES UP and BECOME M-1