Q.

If the speed of light (c) acceleration due to gravity (g) and pressure (p) are taken as the fundamental quantities, then the dimensions of length will be

Moderate

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c2g−1p0

cg0p−1

c−1gp0

cg−1p0

answer is 1.

(Detailed Solution Below)

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Detailed Solution

l∝cαgβpγ⇒L=LT−1αLT−2βML−1T−2γ⇒L=MγLα+β−γT−α−2β−2γ⇒ γ=0,α+β=1 and −α−2β=0⇒ −β=1⇒ β=−1 and α=2 So, l=c2g−1p0Also, we could have done this by taking dimensional formulae for velocity and acceleration and eliminating t.Hence, the correct answer is (1).

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