Question

In the formula $x={3yz}^2$, $x$ and $z$ have dimensions of capacitance and magnetic induction field strength respectively. The dimensions of $y$ in system is :

• A. $M^{-3}{L}^{-2}{T}^4{Q}^4$
• B. $M^{-2}{L}^{-2}{T}^2{Q}^2$
• C. $M^{-3}{L}^{-1}{T}^4{Q}^4$
• D. $M^2{L}^2{T}^{-3}{Q}^{-1}$

Answer 1

The correct option is A $M^{-3}{L}^{-2}{T}^4{Q}^4$

$x=3y{z}^2$

$x=M^{-1}{L}^{-2}{I}^2{T}^4$
$z=M^1{I}^{-1}{T}^{-2}$

Let, $y=M^{\alpha }{L}^{\beta }{T}^{\gamma }{Q}^{\delta }$

$\left(M^{-1}{L}^{-2}{I}^2{T}^4\right)=\left(M^{\alpha }{L}^{\beta }{T}^{\gamma }{Q}^{\delta }\right)\left(M^{+1}{L}^0{I}^{-1}{T}^{-2}\right)$
$IT=Q$
$\alpha =-3,\beta =-2,\gamma =4,\delta =4$
$y=M^{-3}{L}^{-2}{T}^4{Q}^4$