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

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

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 correct?…

Solution