Question

Let x and a stand for distance. Is $\int\limits dx/ \sqrt{a^2-x^2}$ = $\frac{1}{a}$ sin⁻$\frac{a}{x}$ dimensionally correct ?
Concept of Physics - 1 , HC VERMA , Chapter "Introduction to Physics".

Answer 1

Hello Dear.

Given , $\int\limits dx/ \sqrt{a^{2}-x^{2}} = \frac{1}{a}$ sin⁻ $\frac{x}{a}$ 

For LHS :- 

$\int\limits dx/ \sqrt{a^{2}-x^{2}}$ 
Changing into dimension
$\int\limits$ $\frac{L}{ \sqrt{L^2-L^2}}$ 
= [L⁰ ]


For RHS :-

$\frac{1}{a}$ sin⁻ $\frac{a}{x}$
Changing into dimensions
$\frac{1}{L}$
= [L⁻¹]


∵ L.H.S. ≠ R.H.S.

∴ Equation is dimensionally incorrect.


Hope it helps.

Answer 2

Answer:

answer is 1/2 is the correct option

go fot it