Discussion
In the equation A = B/CD2 , if B, C and D have the dimensions of inductive reactance, capacitive reactance and angular frequency respectively, then the dimensions of A are
Answer: C
The dimensions of A are \(M^{0}L^{0}T^{2}\).
Inductive reactance and capacitive reactance are both measured in ohms, so B and C have the same dimensions and \(\frac{B}{C}\) is dimensionless. Angular frequency D has dimensions \(T^{-1}\). Hence
\[ \begin{aligned} [A] &= \frac{[B]}{[C][D]^{2}} = \frac{1}{T^{-2}} \\ &= M^{0}L^{0}T^{2} \end{aligned} \]
\(M^{0}L^{0}T^{-2}\) multiplies by \(D^{2}\) instead of dividing. The options with nonzero powers of M or L forget that the two reactances cancel completely.
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