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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousHard2 minPYQ_2017

PhysicsHardsingle choice

A physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^{2}}{4 π ε_{0}}$ , where [ $c$ is velocity of light, $G$ is universal constant of gravitation, $e$ is charge & $ε_{0}$ is permittivity of free space]:NEET 2017

Options:

Answer:

Solution:

Let $\frac{e^{2}}{4 π ε_{0}} = A = M L^{3} T^{- 2}$

$L = C^{x} G^{y} {(A)}^{z}$

$[L] = {[L T^{- 1}]}^{x} {[M^{- 1} L^{3} T^{- 2}]}^{y} {[M L^{3} T^{- 2}]}^{z}$

$- y + z = 0 \Rightarrow y = z$ ......(i)

$x + 3 y + 3 z = 1$ ......(ii)

$- x - 4 z = 0$ ......(iii)

From (i), (ii) and (iii)

$z = y = \frac{1}{2}, x = - 2$

Stream:NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2017

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