Question

A physical quantity of the dimension of length that can be formed out of c, G and$\frac{e^2}{4\pi {\epsilon }_0}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]

• A. $\frac{1}{c^2}{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$
• B. $c^2{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$
• C. $\frac{1}{c^2}{\left[\frac{e^2}{G4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$
• D. $\frac{1}{c}G\frac{e^2}{4\pi {\epsilon }_0}$

Answer 1

The correct option is A

$\frac{1}{c^2}{\left[G\frac{e^2}{4\pi {\epsilon }_0}\right]}^{\frac{1}{2}}$

Let $\frac{e^2}{4\pi {\epsilon }_0}=A=M{L}^3{T}^{-2}I=C^x{G}^y(A{)}^{z}L=[L{T}^{-1}{]}^x\left[M^{-1}{L}^3{T}^{-2}{]}^y\right[M{L}^3{T}^{-2}{]}^z-y+z=0\Rightarrow y=z.....\left(i\right)x+3y+3z=1....\left(ii\right)-x-4z=0.....\left(iii\right)From\left(i\right),\left(ii\right)and\left(iii\right)z=y=\frac{1}{2},x=-2$