Question

Given that $\int \frac{dx}{\sqrt{2ax-x^2}}=a^n{sin}^{-1}\left[\frac{x-a}{a}\right]$where $a=$constant. Using dimensional analysis, the value of $n$ is:

• A. 1
• B. 0
• C. -1
• D. None of the above

Answer 1

The correct option is B 0

Dimension of a has to be the same as that of $x$ for $x-a$ to be a valid expression in the right side. Hence, $\sqrt{2ax-x^2}$ has the dimensions of $x$ , which implies the dimensions of the numerator and denominator are same on the left hand side. For the term to be dimensionless on the right hand side too, n must be equal to zero.