Question

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

• A. $-2$ in mass, $-2$ in length, $4$ in time and $5$ in charge.
• B. $-3$ in mass, $-2$ in length, $4$ in time and $4$ in charge.
• C. $-4$ in mass, $-5$ in length, $4$ in time and $4$ in charge.
• D. $-3$ in mass, $-2$ in length, $8$ in time and $7$ in charge.

Answer 1

Answer: (B)

$-3$ in mass, $-2$ in length, $4$ in time and $4$ in charge.

Given,

$X=3Y{Z}^2$

Then,

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

$\left[X\right]=\left[C\right]=\left[M^{-1}{L}^{-2}{T}^2{Q}^2\right]$

$\left[Z\right]=\left[B\right]=\left[M{T}^{-1}{Q}^{-1}\right]$

Then,

$\left[Y\right]=\frac{\left[X\right]}{\left[3Z^2\right]}$

$=\frac{\left[M^{-1}{L}^{-2}{T}^2{Q}^2\right]}{[M{T}^{-1}{Q}^{-1}{]}^2}=\left[M^{-3}{L}^{-2}{T}^4{Q}^4\right]$

That is,

$-3$ in mass, $-2$ in length, $4$ in time and $4$ in charge.