Question

If $C$ is capacitance and $Q$ is charge, then the dimension of $\frac{Q^2}{C}$ is same as that of ?

• A. Work
• B. Angular momentum
• C. Force
• D. Torque and energy

Answer 1

Answer: (A), (D)

Torque and energy

Step 1: Given data

capacitance$\to C$

charge$\to Q$

We have to find the dimensions of $\frac{Q^2}{C}$

Step 2: Formula and dimension

Dimension of $\frac{Q^2}{C}$ ,

$$\begin{gathered} \frac{Q^2}{C}=\frac{Q^2}{{\displaystyle \raisebox{1ex}{$Q$}\!\left/ \!\raisebox{-1ex}{$V$}\right.}}\left(\because C=\frac{Q}{V}\right) \\ \Rightarrow \frac{Q^2}{C}=QV \\ \Rightarrow \frac{Q^2}{C}=Q\left(\raisebox{1ex}{$W$}\!\left/ \!\raisebox{-1ex}{$Q$}\right.\right)\left(\because V=\frac{W}{Q}\right) \\ \Rightarrow \frac{Q^2}{C}=W \\ \Rightarrow \frac{Q^2}{C}=F·s\left(WeknowW=F·s\right) \\ \Rightarrow \frac{Q^2}{C}=\left[M{L}^2{T}^{-2}\right] \end{gathered}$$

Explanation of correct option

Dimension of work, $W=\left[M{L}^2{T}^{-2}\right]$

Dimension of torque or energy, ${\rm T}=E=\left[M{L}^2{T}^{-2}\right]$

Therefore option A and option D are correct

Explanation of incorrect option

Dimension of angular momentum, $L=\left[M{L}^2{T}^{-1}\right]$

Dimension of force, $F=\left[ML{T}^{-2}\right]$

Option B and option C are incorrect