First slide

Dimensions of physical quantities

Question

$\int \frac{d x}{\sqrt{2 a x - x^{2}}} = a^{n} \sin^{- 1} (\frac{x}{a} - 1) .$ The value of n is

Moderate

A

0
B

–1
C

1
D

None of these

Solution

Trigonometric function has no dimension.
So, $\frac{x}{a} = \dim e n s i o n l e s s$
Thus, a has the dimensions as x in equation.
RHS has dimension of $\frac{x}{a}$ i.e., dimensionless and hence, $a^{n}$ is dimensionless
$\Rightarrow n = 0$

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