Question

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

• A. $\left[M^{-3}L^{-2}T^{4}Q^{4}\right]$
• B. $\left[M^{-2}L^{-1}T^{5}Q^{3}\right]$
• C. $\left[M^{-1}L^{-2}T^{4}Q^{4}\right]$
• D. $\left[M^{-3}L^{-1}T^{4}Q^{4}\right]$

Answer 1

Answer: (A)

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