(B) The dimensions of the given quantities are:$[L] = ML^2T^{-2}A^{-2}$$[C] = M^{-1}L^{-2}T^4A^2$$[R] = ML^2T^{-3}A^{-2}$Now, let us evaluate the dime

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(B) The dimensions of the given quantities are:$[L] = ML^2T^{-2}A^{-2}$$[C] = M^{-1}L^{-2}T^4A^2$$[R] = ML^2T^{-3}A^{-2}$Now, let us evaluate the dimensions of the expression $\frac{R^2}{L}$:$[R^2] = (ML^2T^{-3}A^{-2})^2 = M^2L^4T^{-6}A^{-4}$$[L] = ML^2T^{-2}A^{-2}$Therefore, the dimensions of $\frac{R^2}{L}$ are:$\frac{[R^2]}{[L]} = \frac{M^2L^4T^{-6}A^{-4}}{ML^2T^{-2}A^{-2}} = ML^2T^{-4}A^{-2}$This matches the given dimensional formula. Thus, the correct expression is $\frac{R^2}{L}$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

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A
$\frac{R}{\sqrt{LC}}$
B
$\frac{R^2}{L}$
C
$\frac{C}{\sqrt{LR}}$
D
$\frac{1}{R}\sqrt{\frac{L}{C}}$

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Dimensional Analysis, Uses and Limitations

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$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

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