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1.Units, Dimensions and Measurement
hard
$\int_{}^{} {\frac{{dx}}{{{{(2ax - {x^2})}^{1/2}}}} = {a^n}{{\sin }^{ - 1}}\left( {\frac{x}{a} - 1} \right)} $ in this formula $n =$ _____
A$1$
B$-1$
C$0$
D$\frac{1}{2}$
Solution
$x$ = length
$\therefore \,[X]\, = \,[L]$ and $ [dx]\, = \,[L]$
$\left[ {\frac{x}{a}} \right]\, =$ dimensionless
$\therefore \,[a] = [x]\, = \,[L]$ $\frac{{[L]}}{{{{[{L^2} – {L^2}]}^{1/2}}}} = [{L^n}]$
$\therefore \,\,n\, = \,0$
$\therefore \,[X]\, = \,[L]$ and $ [dx]\, = \,[L]$
$\left[ {\frac{x}{a}} \right]\, =$ dimensionless
$\therefore \,[a] = [x]\, = \,[L]$ $\frac{{[L]}}{{{{[{L^2} – {L^2}]}^{1/2}}}} = [{L^n}]$
$\therefore \,\,n\, = \,0$
Standard 11
Physics
