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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
Similar Questions
Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :
| List $I$ | List $II$ |
| $P.$ Boltzmann constant | $1.$ $\left[ ML ^2 T ^{-1}\right]$ |
| $Q.$ Coefficient of viscosity | $2.$ $\left[ ML ^{-1} T ^{-1}\right]$ |
| $R.$ Planck constant | $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$ |
| $S.$ Thermal conductivity | $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$ |
Codes: $ \quad \quad P \quad Q \quad R \quad S $
