Q. In the equation $X = 3YZ^{2}$, $X$ and $Z$ have dimensions of capacitance and magnetic induction respectively. In MKSQ system, the dimensional formula of $Y$ is
A) [$M^{- 3}L^{- 2}T^{- 2}Q^{- 4}$]
B) [$ML^{- 2}$]
C) [$M^{- 3}L^{- 2}{Q^{4}T}^{8}$]
D) [$M^{- 3}L^{- 2}{Q^{4}T}^{4}$]
Explanation
[capacitance $X$]=[$M^{- 1}L^{- 2}T^{2}Q^{2}$] [Magnetic induction $Z$] = [$MT^{- 1}Q^{- 1}$] [$Z^{2}$]=[$M^{2}T^{- 2}Q^{- 2}$] Given, $X = 3YZ^{2}$ or $Y = \frac{X}{3Z^{2}}$ or $\lbrack Y\rbrack = \frac{\lbrack X\rbrack}{\lbrack Z\rbrack^{2}}$ $\therefore\ \ \ \ \lbrack Y\rbrack$ =$\frac{\lbrack M^{- 1}L^{- 2}T^{2}Q^{2}\rbrack}{\lbrack M^{2}T^{- 2}Q^{- 2}\rbrack} = \lbrack M^{- 3}L^{- 2}T^{4}Q^{4}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.