Physics, asked by jahnavi4318, 9 months ago

find the dimensions of G from
f = Gm1m2 \div r2

Answers

Answered by Ekaro
8

Given :

We have been provided formula of gravitational force.

\dag\:\boxed{\bf\red{F=\dfrac{Gm_1m_2}{r^2}}}

To Find :

We have to find dimensions of universal gravitational constant.

SoluTion :

Dimension Formula :

\longrightarrow\tt\:\blue{Force(F)=[M^1L^1T^{-2}]}

\longrightarrow\tt\:\green{Mass(m)=[M^1]}

\longrightarrow\tt\:\pink{Distance(r)=[L^1]}

Let's calculate

:\implies\rm\:F=\dfrac{Gm_1m_2}{r^2}

:\implies\rm\:G=\dfrac{F\times r^2}{m_1m_2}

:\implies\rm\:G=\dfrac{[M^1L^1T^{-2}]\times [L^1]^2}{[M^1][M^1]}

:\implies\rm\:G=\dfrac{[M^1L^3T^{-2}]}{[M^2]}

:\implies\underline{\boxed{\bf{\purple{G=[M^{-1}L^3T^{-2}]}}}}

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