The dimensions of the quantity 1-0 e 2- hc ise - charge of electronh - planck-s constant c- velocity of light-0- permittivity of free spaceA- ML -1 L -3 T 4 A 2B- M -1 L -3 T 2 AC- M 0 L 0 T 0 A 0D- ML 3 T -4 A -2

The correct option is C M^0 L^0 T^0 A^0[hc] = [ML^2 T^ 2] [L] = [ML^3 T^ 2] [e^2/ϵ_0] = [MLT^ 2][L^2] = [ML^3 T^ 2] [1/ϵ_0e^2/hc] = M^0 L^0 T^0 A^0 ...

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Standard XII

Physics

Flux as the Flow

The dimension...

Question

The dimensions of the quantity $\frac{1}{ϵ_{0}} \frac{e^{2}}{h c}$ is
e = charge of electron
h = planck’s constant
c = velocity of light
$ϵ_{0}$ = permittivity of free space

M^{- 1} L^{- 3} T^{2} A

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M^{0} L^{0} T^{0} A^{0}

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M L^{3} T^{- 4} A^{- 2}

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M L^{- 1} L^{- 3} T^{4} A^{2}

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Solution

The correct option is B $M^{0} L^{0} T^{0} A^{0}$
$[h c] = [M L^{2} T^{- 2}] [L] = [M L^{3} T^{- 2}] [\frac{e^{2}}{ϵ_{0}}] = [M L T^{- 2}] [L^{2}] = [M L^{3} T^{- 2}] [\frac{1}{ϵ_{0}} \frac{e^{2}}{h c}] = M^{0} L^{0} T^{0} A^{0}$

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The dimensions of the quantity 1ϵ0e2hc is e = charge of electron h = planck’s constant c = velocity of light ϵ0 = permittivity of free space

The correct option is B M0L0T0A0[hc]=[ML2T−2][L]=[ML3T−2][e2ϵ0]=[MLT−2][L2]=[ML3T−2][1ϵ0e2hc]=M0L0T0A0

The dimensions of the quantity $\frac{1}{ϵ_{0}} \frac{e^{2}}{h c}$ is
e = charge of electron
h = planck’s constant
c = velocity of light
$ϵ_{0}$ = permittivity of free space

The correct option is B $M^{0} L^{0} T^{0} A^{0}$
$[h c] = [M L^{2} T^{- 2}] [L] = [M L^{3} T^{- 2}] [\frac{e^{2}}{ϵ_{0}}] = [M L T^{- 2}] [L^{2}] = [M L^{3} T^{- 2}] [\frac{1}{ϵ_{0}} \frac{e^{2}}{h c}] = M^{0} L^{0} T^{0} A^{0}$