Question

In the equation $X=2Y{Z}^2$, $X$ and $Z$ are dimensions of capacitance and magnetic induction respectively. In MKSQ system, the dimensional formula for $Y$ is

• A. $\left[M^{-3}{L}^{-2}{T}^{-2}{Q}^{-4}\right]$
• B. $\left[M{L}^{-2}\right]$
• C. $\left[M^{-3}{L}^{-2}{Q}^4{T}^8\right]$
• D. $\left[M^{-3}{L}^{-2}{Q}^4{T}^4\right]$

Answer 1

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

Dimensionally: $\left[Y\right]=\frac{\left[X\right]}{\left[Z^2\right]}=\frac{M^{-1}{L}^{-2}{T}^4{A}^2}{M^2{T}^{-4}{A}^{-2}}=M^{-3}{L}^{-2}{T}^8{A}^4$
But we have, $A=\frac{Q}{T}$
$\left[Y\right]=M^{-3}{L}^{-2}{Q}^4{T}^4$