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A physical quantity of the dimension of length

A physical quantity of the dimensions of length that can be formed out of c, G and \frac{e^{2}}{4\pi \varepsilon _{o}} is (c is velocity of light, G is universal constant of gravitation and e is charge)  

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A Avinash Dongre

To solve these questions first write dimentions of all the given quantity in term of fundamental quantity and then find relation between them.

herefore T= 2pi sqrt{l/g}

- wherein

T= time : period

l= length

g=: acceleration : due: to: gravity

 

 \frac{e^{2}}{4\pi\epsilon _{^{\circ}} }= [F \times d^{2}]= Mc^{3}T^{-2}

G= ML^{3}T^{-2}

C= L^{-1}

l\propto(\frac{e^{2}}{4\pi \epsilon _{^{\circ}}})^{P}G^{q}C^{r}

[L^{1}]= [MC^{3}T^{-2}]^{P} [M^{-1}L^{3}T^{-2}]^{q} [LT^{-1}]^{r}

on comparing both sides we get

P=\frac{1}{2}, q=\frac{1}{2}, r =-2

\therefore l= \frac{1}{C^{2}}[ \frac{Ge^{2}}{4\pi \epsilon _{^{\circ}}} ]^{1/2}

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