Q213 / 240 · KCET 2026 · Physics
Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and electric current (A) given in List-II.
List-I List-II (a) Torque (i) $[M^{-1}L^{-2}T^{4}A^{2}]$ (b) Gravitational constant (ii) $[M^{1}L^{2}T^{-1}]$ (c) Capacitance (iii) $[M^{-1}L^{3}T^{-2}]$ (d) Planck's constant (iv) $[M^{1}L^{2}T^{-2}]$
Codes:
| List-I | List-II |
|---|---|
| (a) Torque | (i) $[M^{-1}L^{-2}T^{4}A^{2}]$ |
| (b) Gravitational constant | (ii) $[M^{1}L^{2}T^{-1}]$ |
| (c) Capacitance | (iii) $[M^{-1}L^{3}T^{-2}]$ |
| (d) Planck's constant | (iv) $[M^{1}L^{2}T^{-2}]$ |
- Aa - iv, b - ii, c - iii, d – i
- Correct answerBa - iv, b - iii, c - i, d – ii
- Ca - iv, b - i, c - iii, d – ii
- Da - ii, b - i, c - iii, d – iv
Solution
Torque $\tau = \text{Force} \times \text{Distance}$
$[\tau] = [MLT^{-2}][L] = [M^{1}L^{2}T^{-2}]$
Gravitational constant $G = \dfrac{Fr^{2}}{m_{1}m_{2}}$
$[G] = \dfrac{[MLT^{-2}][L^{2}]}{[M^{2}]} = [M^{-1}L^{3}T^{-2}]$
Capacitance $C = \dfrac{Q}{V} = \dfrac{Q^{2}}{W}$
$[C] = \dfrac{[AT]^{2}}{[ML^{2}T^{-2}]} = [M^{-1}L^{-2}T^{4}A^{2}]$
Planck's constant $h = \dfrac{E}{\nu}$
$[h] = \dfrac{[ML^{2}T^{-2}]}{[T^{-1}]} = [M^{1}L^{2}T^{-1}]$
Thus, the correct matching is a - iv, b - iii, c - i, d - ii.
Answer: a - iv, b - iii, c - i, d – ii
$[\tau] = [MLT^{-2}][L] = [M^{1}L^{2}T^{-2}]$
Gravitational constant $G = \dfrac{Fr^{2}}{m_{1}m_{2}}$
$[G] = \dfrac{[MLT^{-2}][L^{2}]}{[M^{2}]} = [M^{-1}L^{3}T^{-2}]$
Capacitance $C = \dfrac{Q}{V} = \dfrac{Q^{2}}{W}$
$[C] = \dfrac{[AT]^{2}}{[ML^{2}T^{-2}]} = [M^{-1}L^{-2}T^{4}A^{2}]$
Planck's constant $h = \dfrac{E}{\nu}$
$[h] = \dfrac{[ML^{2}T^{-2}]}{[T^{-1}]} = [M^{1}L^{2}T^{-1}]$
Thus, the correct matching is a - iv, b - iii, c - i, d - ii.
Answer: a - iv, b - iii, c - i, d – ii
Hence, the correct answer is option: 'B'.