Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,

<p>The capacitance (in farads) is defined as the ratio of charge to potential difference. Let's go through the steps:</p> <p><p>Capacitance is given by: </p> <p>$C = \frac{Q}{V}$ </p> <p>where:</p></p> <p><p>$ Q $ is the charge with dimensional symbol $ C $.</p></p> <p><p>$ V $ is the potential difference.</p></p> <p><p>Voltage (potential difference) is defined as energy per unit charge: </p> <p>$V = \frac{W}{Q}$ </p> <p>where:</p></p> <p><p>$ W $ is energy with dimensions: </p> <p>$[W] = [M L^2 T^{-2}]$</p></p> <p><p>Therefore, the dimensions of voltage are: </p> <p>$[V] = \frac{[ML^2T^{-2}]}{[C]}$</p></p> <p><p>Now, substitute this back into the expression for capacitance: </p> <p>$[C] = \frac{[Q]}{[ML^2T^{-2}]/[C]} = \frac{[C]^2}{ML^2T^{-2}}$</p></p> <p><p>Simplifying gives: </p> <p>$[C] = [C^2 M^{-1}L^{-2}T^2]$</p></p> <p>Comparing with the given options, we see that Option C is: </p> <p>$[F] = [C^2 M^{-1}L^{-2}T^2]$</p> <p>Thus, the correct dimensional formula for the capacitance in farads is given by Option C.</p>