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1.Units, Dimensions and Measurement
medium
જો $x$ અને $a$ અંતર હોય તો પરિમાણિક રીતે સાચા આપેલ સમીકરણમાં $n$ નું મૂલ્ય કેટલું હશે?
$\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
