If $x$ and $a$ stand for distance, then for what value of $n$ is the given equation dimensionally correct? The equation is $\int \frac{d x}{\sqrt{a^{2}-x^{n}}}=\sin ^{-1} \frac{x}{a}$.

Question

Aicharya · Accepted Answer

Here, $x^{n}$ has the same dimensions as $a^{2}$. Thus, $n=2$ will make the expression dimensionally correct.

If \(x\) and \(a\) stand for distance, then for what value of \(n\) is the given equation dimensionally…

Solution