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CGP EDU Academic Team
Published on: September 12, 2026
Match the physical quantities given in column I with dimensions in column II.
Column-I | Column-II |
(i) Torque | (p) |
(ii) Angular momentum | (q) |
(iii) Latent heat | (r) |
(iv) Surface tension | (s) |
(v) Light year | (t) |
(u) |
Text Solution
Verified by ExpertsThe correct answer is:
B
Let's analyze each quantity in Column I and match it with the appropriate dimensions in Column II:
(i) Torque: Torque is given by the formula \( \tau = r \times F \). Dimensions of torque are \( [M][L^2][T^{-2}] = [ML^2T^{-2}] \). Therefore, it matches with (q).
(ii) Angular momentum: Angular momentum is given by \( L = r \times p \) where \( p \) is momentum. The dimensions are also \( [M][L^2][T^{-1}] = [ML^2T^{-1}] \). Therefore, it matches with (p).
(iii) Latent heat: Latent heat is defined as the heat absorbed/released per unit mass. The dimensions are \( [M^0][L^2][T^{-2}] = [M^0L^2T^{-2}] \). Therefore, it matches with (r).
(iv) Surface tension: Surface tension is defined as force per unit length, which has dimensions \( [M^0][L^1][T^{-2}] = [M^0LT^{-2}] \). Therefore, it matches with (s).
(v) Light year: A light year is a unit of distance, with dimensions given as \( [M^0][L^1][T^0] = [M^0L^1T^0] \). Therefore, it matches with (t).
Thus, we have: \( (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s), (v)-(t) \) which corresponds to Option B.
(i) Torque: Torque is given by the formula \( \tau = r \times F \). Dimensions of torque are \( [M][L^2][T^{-2}] = [ML^2T^{-2}] \). Therefore, it matches with (q).
(ii) Angular momentum: Angular momentum is given by \( L = r \times p \) where \( p \) is momentum. The dimensions are also \( [M][L^2][T^{-1}] = [ML^2T^{-1}] \). Therefore, it matches with (p).
(iii) Latent heat: Latent heat is defined as the heat absorbed/released per unit mass. The dimensions are \( [M^0][L^2][T^{-2}] = [M^0L^2T^{-2}] \). Therefore, it matches with (r).
(iv) Surface tension: Surface tension is defined as force per unit length, which has dimensions \( [M^0][L^1][T^{-2}] = [M^0LT^{-2}] \). Therefore, it matches with (s).
(v) Light year: A light year is a unit of distance, with dimensions given as \( [M^0][L^1][T^0] = [M^0L^1T^0] \). Therefore, it matches with (t).
Thus, we have: \( (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s), (v)-(t) \) which corresponds to Option B.
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