Physics

# Consider the following two statements A and B. Identify the correct answer.A) The quantity $\dfrac { { e }^{ 2 } }{ { \epsilon }_{ 0 }ch }$ is dimensionless.B) $\dfrac { 1 }{ \sqrt { { \mu }_{ 0 }{ \epsilon }_{ 0 } } }$ has the dimensions of velocity and is numerically equal of velocity of light.

Both A and B are true

##### SOLUTION
Dimensions of permittivity ${ \epsilon }_{ 0 }$: ${ A }^{ 2 }{ T }^{ 4 }{ M }^{ -1 }{ L }^{ 3 }$
Dimensions of ${ e }^{ 2 }$ : ${ A }^{ 2 }{ T }^{ 2 }$
Dimensions of $c$ : $L{ T }^{ -1 }$
Dimensions of $h$ : $M{ L }^{ 2 }{ T }^{ -1 }$
Therefore, dimensions of the given expression:
$\dfrac { { A }^{ 2 }{ T }^{ 2 } }{ ({ A }^{ 2 }{ T }^{ 4 }{ M }^{ -1 }{ L }^{ 3 })\times (L{ T }^{ -1 })\times (M{ L }^{ 2 }{ T }^{ -1 }) } =1$ which is dimensionless.

Hence, Statement A is true.
In statement B, the expression given is for the speed of light.Hence, it has dimensions of velocity.

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Single Correct Medium Published on 18th 08, 2020
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