First slide

Dimensions of physical quantities

Question

In the equation $\int \frac{d x}{\sqrt{2 a x - x^{2}}} = a^{n} \sin^{- 1} (\frac{x}{a} - 1)$ . Find the value of $n$ .

Moderate

A

n=0
B

n=1
C

n=2
D

n=5

Solution

$[\frac{d x}{\sqrt{2 a x - x^{2}}}]$ is dimensionless
Therefore, $[a^{n} \sin^{- 1} (\frac{x}{a} - 1)]$ should also be dimensionless.
Hence, n=0

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