Question

Express $L$ (length) in terms of $G,h$ and $c$ -
Here $G$ is universal gravitational constsnt, $h$ is plank's constant, $c$ is speed of light

• A. $G^{-\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{\frac{1}{2}}$
• B. $G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{3}{2}}$
• C. $G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{5}{2}}$
• D. $Ghc$

Answer 1

The correct option is B $G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{3}{2}}$

$L\propto G^x{h}^y{c}^z....\left(i\right)$
$M^0{L}^1{T}^0\propto \left[M^{-1}{L}^3{T}^{-2}{]}^x\right[M{L}^2{T}^{-1}{]}^y[L{T}^{-1}{]}^z$
$M^0{L}^1{T}^0\propto M^{-x+y}{L}^{3x+2y+z}{T}^{-2x-y-z}$
$-x+y=0\Rightarrow y=x$
$3x+2y+z=1\Rightarrow 5x+z=1$
$-2x-y-z=0\Rightarrow -3x-z=0$
$-3x=z$
$2x=1\Rightarrow x=\frac{1}{2}$
$y=x=\frac{1}{2}$
$z=-3x=-\frac{3}{2}$
$L\propto G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{3}{2}}$