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Dimensional Analysis

Find the dime...

Question

Find the dimensions of G in the equation $F = \frac{G m_{1} m_{2}}{r^{2}}$ ; where F is the force of gravitational attraction between two bodies of point masses $m_{1}$ and $m_{2}$ , 'r' is the distance of separation between them.

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Solution

The gravitational force acting between the two bodies is given by:
$F = G \frac{m_{1} m_{2}}{r^{2}}$

$G = \frac{F r^{2}}{m_{1} m_{2}}$

The dimension of the force is $[M L T^{- 2}]$

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

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