Physics And Measurement Question 24
Question: Assertion: The quantity $ (1/\sqrt{{\mu _{0}}{\varepsilon _{0}}}) $ is dimensionally equal to velocity and numerically equal to velocity of light. Reason: $ {\mu _{0}} $ is permeability of free space and $ {\varepsilon _{0}} $ is the permittivity of free space.
Options:
A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
C) If assertion is true but reason is false.
D) If the assertion and reason both are false.
E) If assertion is false but reason is true.
Show Answer
Answer:
Correct Answer: B
Solution:
Both assertion and reason are true but reason is not the correct explanation of assertion. $ [{\varepsilon _{0}}]=[{{M}^{-1}}{{L}^{-3}}T^{4}I^{2}] $ , $ [{\mu _{0}}]=[ML{{T}^{-2}}{{I}^{-2}}] $
$ \Rightarrow \frac{1}{\sqrt{({\mu _{0}}/4\pi )\times 4\pi E _{0}}}=\sqrt{\frac{9\times 10^{9}}{{{10}^{-7}}}}=\sqrt{9\times 10^{16}} $
$ =3\times 10^{8}m/s. $ Therefore $ \frac{1}{\sqrt{{\mu _{0}}{\varepsilon _{0}}}} $ has dimension of velocity and numerically equal to velocity of light.
