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Q.

A physical quantity of the dimensions of length that can be formed out of c, G and $\frac{e^{2}}{4 {πϵ}_{0}}$ is [c is velocity of light, G is universal constant of gravitation and e is charge]:

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a

$\frac{1}{c} G \frac{e^{2}}{4 π \in_{0}}$

b

$\frac{1}{c^{2}} {[\frac{e^{2}}{G 4 π \in_{0}}]}^{1 / 2}$

c

$\frac{1}{c^{2}} {[G \frac{e^{2}}{4 {πϵ}_{0}}]}^{1 / 2}$

d

$c^{2} {[G \frac{e^{2}}{4 π ϵ_{0}}]}^{1 / 2}$

answer is B.

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Detailed Solution

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$C = {LT}^{- 1}; G = M^{- 1} L^{3} T^{- 2}; \frac{e^{2}}{4 {πε}_{0}} = {ML}^{3} T^{- 2}$

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A physical quantity of the dimensions of length that can be formed out of c, G and e24πϵ0 is [c is velocity of light, G is universal constant of gravitation and e is charge]: