Question

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

• A. $C/g$
• B. $C/P$
• C. $PCg$
• D. $C^2/g$

Answer 1

The correct option is D $C^2/g$

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, $z=0$ ; $x+y=1$ ; $-x-2y=0$

$-2y+y=1$ $\Rightarrow$ $x=-2y$.

$\Rightarrow$ $y=-1\Rightarrow x=2$

$\therefore$ $dim\left(length\right)=c^x{g}^y{p}^z=c^2{g}^{-1}{p}^0=\frac{c^2}{g}$.