Question

If $C$, the velocity of light, $g$ the acceleration due to gravity and $P$ the atmospheric pressure be the fundamental quantities in MKS system, then the dimensions of length will be same as that of

• A. $\frac{C}{g}$
• B. $\frac{C}{P}$
• C. PCg
• D. $\frac{C^2}{g}$

Answer 1

Answer: (D)

Let $C^{x} g^{y} P^{z}$ be dimensions of length.
$\Rightarrow \left[ M ^{0} LT ^{-1}\right]^{ x }\left[ M ^{0} LT ^{-2}\right]^{ y }\left[ ML ^{-1} T ^{-2}\right]^{2}= M ^{0} LT ^{0}$
$\Rightarrow $ Comparing powers of $M, L$ and $T$.
We get, $z=0 ; x+y=1 ;-x-2 y=0$
$-2 y+y=1 \Rightarrow x=-2 y$
$\Rightarrow y =-1 \Rightarrow x =2$
$\therefore dim($ length $)=c^{x} g^{y} p^{z}$
$=c^{2} g^{-1} p^{0}=\frac{c^{2}}{g}$.