Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Physical Quantities) | (Dimensions) | ||
| (A) | Capacitance | (I) | \( [M^{1}L^{2}T^{-3}A^{-1}] \) |
| (B) | Polarisation | (II) | \( [L^{-2}AT] \) |
| (C) | Electric Potential | (III) | \( [M^{-1}L^{-2}T^{4}A^{2}] \) |
| (D) | Volume charge density | (IV) | \( [L^{-3}AT] \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (III), (B) - (II), (C) - (I), (D) - (IV)
The dimensions of each quantity follow from its defining relation, starting from charge \( [Q] = [AT] \) and energy \( [ML^{2}T^{-2}] \).
(A) Capacitance — this matches (III) \( [M^{-1}L^{-2}T^{4}A^{2}] \). Capacitance is charge per unit potential, \( C = Q/V \).
\( \displaystyle [C] = \frac{[AT]}{[ML^{2}T^{-3}A^{-1}]} = [M^{-1}L^{-2}T^{4}A^{2}] \)
(B) Polarisation — this matches (II) \( [L^{-2}AT] \). Polarisation is the dipole moment per unit volume, so its unit is \( \mathrm{C\,m/m^{3}} = \mathrm{C\,m^{-2}} \), the same as surface charge density.
(C) Electric Potential — this matches (I) \( [M^{1}L^{2}T^{-3}A^{-1}] \). Potential is work done per unit charge.
\( \displaystyle [V] = \frac{[ML^{2}T^{-2}]}{[AT]} = [ML^{2}T^{-3}A^{-1}] \)
(D) Volume charge density — this matches (IV) \( [L^{-3}AT] \). It is charge per unit volume, \( \mathrm{C\,m^{-3}} \).
Note: This question is from beyond the NCERT textbook and it appears to be out of the CUET 2026 Physics syllabus.