Physical World Units and Measurements - Result Question 29

31. The dimensional formula for permeability $\mu$ is given by

(a) $[MLT^{-2} A^{-2}]$

[1991]

(b) $[M^{0} L^{1} T]$

(c) $[M^{0} L^{2} T^{-1} A^{2}]$

(d) None of the above

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Answer:

Correct Answer: 31. (a)

Solution:

  1. (a) Permeability of free space,

$ \mu_0=\frac{2 \pi \times \text{ force } \times \text{ distance }}{(\text{ current })^{2} \times \text{ length }} $

So, dimensional formula

$ \mu_0=\frac{[MLT^{-2}][L]}{[A^{2}][L]}=[MLT^{-2} A^{-2}] $

Also find the dimensional formula by using the relation,

Speed of light, $c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$