Question

If in the formula $X=3Y{Z}^2$, the dimensions of $X$ and $Z$ are those of the capacitance and magnetic induction, then the dimensions of Y are :

• A. $M^{-3}{L}^{-2}{T}^8{A}^4$
• B. $M^{-3}{L}^{-2}{T}^4{A}^4$
• C. $M^{-3}{L}^{-2}{T}^{-4}{A}^{-4}$
• D. $M^{-3}{V}^{-2}{T}^{-8}{A}^{-4}$

Answer 1

Answer: (A)

$M^{-3}{L}^{-2}{T}^8{A}^4$

$\left[Y\right]=\frac{\left[X\right]}{{\left[Z\right]}^2}=\frac{\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]}{{\left[M^1{T^{-2}A}^{-1}\right]}^2}$
$\left[Y\right]=\left[M^{-3}{L}^{-2}{T}^8{A}^4\right]$