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:


ANSWER

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


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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