Question

In the formula $X=3Y{Z}^2$, $X$ and $Z$ have dimensions of capacitance and magnetic induction, respectively. What are the dimensions of $Y$ in $MKSQ$ system?

• A. $\left[M^{-3}{L}^{-2}{T}^4{Q}^4\right]$
• B. $\left[M^2{L}^{-2}{T}^4{Q}^4\right]$
• C. $\left[M^{-2}{L}^{-2}{T}^3{Q}^4\right]$
• D. $\left[M^{-3}{L}^{-1}{T}^3{Q}^4\right]$

Answer 1

The correct option is A $\left[M^{-3}{L}^{-2}{T}^4{Q}^4\right]$

The dimension of capacitor is,
$C=\left[M^{-1}{L}^{-2}{T}^2{Q}^2\right]$

The dimension of magnetic induction is,
$B=\left[M{T}^{-1}{Q}^{-1}\right]$

Given, $X=3Y{Z}^2$

$Y=\frac{X}{3Z^2}$

Put the dimension of respective quantity
$\left[Y\right]=\frac{\left[M^{-1}{L}^2{T}^2{Q}^2\right]}{[M{T}^{-1}{Q}^{-1}{]}^2}=\left[M^{-3}{L}^{-2}{T}^4{Q}^4\right]$