Physics

# If the speed of light (c), acceleration due to gravity (g) and pressure (p) are taken as fundamental units, the dimensions of gravitational constant (G) are:

$c^0g^2p^{-1}$

##### SOLUTION
Dimension of $G= M^{-1}L^3T^{-2}$
$[c] = [LT^{-1}]$
$[g] = [LT^{-2}]$
$[p] = [ML^{-1}T^{-2}]$
Equate dimensions
$[M^{-1}L^3T^{-2}] = [LT^{-1}]^\alpha [LT^{-2}]^\beta [ML^{-1}T^{-2}]^\gamma$
$-1 = \gamma$
$3 = \alpha + \beta - \gamma$
$\alpha + \beta =2$                                  (1)
And, $-2 = -\alpha -2\beta -2\gamma$
$\alpha + 2\beta =4$                               (2)
Solving (1) and (2) we get,
$\alpha =0, \beta =2$
$\therefore Dimension = c^0g^2p^{-1}$

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Single Correct Medium Published on 18th 08, 2020
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