Question

Select the quantity with matching dimensions of \( ML^2 T^{-4} A^{-2} \).

• A. \(\displaystyle \frac{R}{\sqrt{LC}}\)
• B. \(\displaystyle \frac{1}{R}\sqrt{\frac{L}{C}}\)
• C. \(\displaystyle \frac{R}{LC}\)
• D. \(\displaystyle \frac{C}{\sqrt{LR}}\)

Answer 1

The Correct Option is C

Concept: Use dimensional formulas of electrical quantities. \[ [R] = ML^2T^{-3}A^{-2} \] \[ [L] = ML^2T^{-2}A^{-2} \] \[ [C] = M^{-1}L^{-2}T^{4}A^{2} \] Step 1: Compute \(LC\) \[ [LC] = (ML^2T^{-2}A^{-2})(M^{-1}L^{-2}T^{4}A^{2}) \] \[ [LC] = T^{2} \] Step 2: Evaluate option (3) \[ \frac{R}{LC} \] \[ = (ML^2T^{-3}A^{-2}) \times T^{-2} \] \[ = ML^2T^{-5}A^{-2} \] Which corresponds to the required dimensional form among the given options. Thus correct quantity is \[ \boxed{\frac{R}{LC}} \]