Which physical quantity is represented by $\mathrm{M}^{1} \mathrm{~L}^{3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ ? (a) Resistivity (b) Resistance (c) conductance (d) conductivity

The dimensional formula for resistivity, denoted by \(\rho\), is: $$\rho = \frac{\mathrm{M}^{0} \mathrm{L}^{3} \mathrm{T}^{-3} \mathrm{A}^{-2}}{\mathrm{M}^{0} \mathrm{L}^{1} \mathrm{T}^{0} \mathrm{A}^{0}} = \mathrm{M}^{0} \mathrm{L}^{3-1} \mathrm{T}^{-3} \mathrm{A}^{-2} = \mathrm{M}^{0} \mathrm{L}^{2} \mathrm{T}^{-3} \mathrm{A}^{-2}$$

The dimensional formula for resistance, denoted by R, is: $$R = \frac{\mathrm{M}^{0} \mathrm{L}^{3} \mathrm{T}^{-3} \mathrm{A}^{-2}}{\mathrm{M}^{0} \mathrm{L}^{2} \mathrm{T}^{0} \mathrm{A}^{0}} = \mathrm{M}^{0} \mathrm{L}^{3-2} \mathrm{T}^{-3} \mathrm{A}^{-2} = \mathrm{M}^{0} \mathrm{L}^{1} \mathrm{T}^{-3} \mathrm{A}^{-2}$$

The dimensional formula for conductance, denoted by G, is: $$ G = \frac{1}{R} \implies G = \mathrm{M}^{0} \mathrm{L}^{-1} \mathrm{T}^{3} \mathrm{A}^{2}$$

The dimensional formula for conductivity, denoted by \(\sigma\), is: $$ \sigma = \frac{1}{\rho} \implies \sigma = \mathrm{M}^{0} \mathrm{L}^{-2} \mathrm{T}^{3} \mathrm{A}^{2} $$ # Step 2: Compare the given formula with each option # Now, we will compare the given dimensional formula \(\mathrm{M^{1}L^{3}T^{-3}A^{-2}}\) with the dimensional formulas of the given options. _resistivity_: \(\mathrm{M^{0}L^{2}T^{-3}A^{-2}}\) _resistance_: \(\mathrm{M^{0}L^{1}T^{-3}A^{-2}}\) _conductance_: \(\mathrm{M^{0}L^{-1}T^{3}A^{2}}\) _conductivity_: \(\mathrm{M^{0}L^{-2}T^{3}A^{2}}\) None of the given options match with the dimensional formula \(\mathrm{M^{1}L^{3}T^{-3}A^{-2}}\). Therefore, the given dimensional formula does not represent any of the given physical quantities (resistivity, resistance, conductance, or conductivity).