SATHEE: Physical World Units and Measurements - Result Question 13

Physical World Units and Measurements - Result Question 13

13. The dimensions of $(μ_{0} ϵ_{0})^{\frac{- 1}{2}}$ are

(a) $[L^{1 / 2} T^{- 1 / 2}]$

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

(c) $[L T^{- 1}]$

(d) $[L^{- 1 / 2} T^{1 / 2}]$

[2012M, 2011]

Show Answer

Answer:

Correct Answer: 13. (c)

Solution:

(c) $(μ_{0} ε_{0})^{- 1 / 2} = \frac{1}{\sqrt{μ_{0} ε_{0}}} \Rightarrow c =$ speed of light where $ε_{0} =$ permittivity of free space

$μ_{0} =$ permeability of free space

So dimensions of $(μ_{0} ε_{0})^{- 1 / 2}$ will be $[L T^{- 1}]$

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