First slide

Dimensions of physical quantities

Question

Let $x a n d a$ stand for distance. Is $\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}$ dimensionally correct?

Moderate

A

Yes
B

No
C

Can't say
D

None of the above

Solution

$[\frac{d x}{\sqrt{a^{2} - x^{2}}}]$ is dimensionless.
$[\frac{1}{a} \sin^{- 1} (\frac{a}{x})]$ has dimensions of $[L^{- 1}]$

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