Let x and a stand for distance. Is ∫ a 2 − x 2 d x = a 1 sin − 1 x a dimensionally correct?

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousMedium2 minQB

PhysicsMediumsingle choice

Let $x$ and $a$ stand for distance. Is $\int \frac{d x}{a ^{2} - x ^{2}} = \frac{1}{a} sin^{- 1} \frac{a}{x}$ dimensionally correct?

Options:

Answer:

Solution:

$\frac{d x}{a ^{2} - x ^{2}}$
is dimensionless, while
$\frac{1}{a} sin^{- 1} (\frac{a}{x})$
has the dimension of $[L^{- 1}]$ .
The two sides do not match, so the equation is dimensionally incorrect.

Stream:JEESubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: QB

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