Question

If $y=a^{3} \sin ^{-1}\left(\frac{x}{b}-1\right)$, where $y$ is in metre. Then,

• A. the dimensions of $a$ is $\left[M^{0} L^{\frac{1}{3}} T^{0}\right]$
• B. the unit of $\sin ^{-1}\left(\frac{x}{b}-1\right)$ is radian
• C. the dimensions of $x$ are same as those of $b$
• D. the unit of $a$ is metre

Answer 1

Answer: (A), (B), (C)

(1) Here, $\sin ^{-1}\left(\frac{x}{b}-1\right)$ is dimensionless.
(2) Let $\sin ^{-1}\left(\frac{x}{b}-1\right)=\theta$
$\therefore \sin \theta=\left(\frac{x}{b}-1\right)$
Here, $\theta$ should be in radian.
So, the unit of $\sin ^{-1}\left(\frac{x}{b}-1\right)$ is radian.
(3) $\therefore$ Dimensions of $\frac{x}{b}=$ Dimensions of $1=$ Dimensionless.
$\therefore$ Dimension of $x=$ Dimensions of $b$.