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KCET · Physics · Units and Dimensions

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-IList-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:

  1. A a - iv, b - ii, c - iii, d – i
  2. B a - iv, b - iii, c - i, d – ii
  3. C a - iv, b - i, c - iii, d – ii
  4. D a - ii, b - i, c - iii, d – iv
Verified Solution

Answer & Solution

Correct Answer

(B) a - iv, b - iii, c - i, d – ii

Step-by-step Solution

Detailed explanation

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