If x and a stand for distance then for what value of n is given equation dimensionally correc

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1.Units, Dimensions and Measurement

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

A

$0$

B

$2$

C

$-\,2$

D

$1$

Solution

$\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\sin ^{-1} \frac{x}{a}$

terms in a equation or terms having arithematic operations of addition and subtraction should have same dimensions.

$\Rightarrow \ln a^{2}-x^{n}$

$\operatorname{dim}\left(a^{2}\right)=\operatorname{dim}\left(x^{n}\right)$

$L^{2}=L^{n} \Rightarrow[n=2]$

Standard 11

Physics

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