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Q.

The dimension of e2/4πε0hc, where e,ε0, h and c are electric charge, electric permittivity of free space, Planck's constant and velocity of light in vacuum, respectively, is

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a

M0L0T0

b

M1L0T0

c

M0L1T0

d

M0L0T1

answer is A.

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Detailed Solution

[e]=[AT] , ε0=M−1L−3T4A2 , [h]=ML2T−1 and [c]=LT−1e24π∈0hc=A2T2M−1L−3T4A2×ML2T−1×LT−1=M0L0T0To calculate ∈0, we can use the formula F=q1q24πε0r2
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The dimension of e2/4πε0hc, where e,ε0, h and c are electric charge, electric permittivity of free space, Planck's constant and velocity of light in vacuum, respectively, is