Published by:
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:
C
Step 1: Identify the dimensions of each quantity in Column-I:
• Torque (i): Dimensions are $[M][L^2][T^{-2}]$ which corresponds to angular momentum.
• Angular momentum (ii): Dimensions are $[M][L^2][T^{-1}]$.
• Latent heat (iii): Dimensions are $[M^0][L^0][T^{-2}]$, which corresponds to energy per unit mass, typically measured in Joules per kg ($J/kg$).
• Surface tension (iv): Dimensions are $[M^0][L^1][T^{-2}]$, equivalent to force per unit length.
• Light year (v): This is a measure of distance and has dimensions $[M^0][L^1][T^0]$.
Step 2: Match these dimensions with Column-II:
(i) Torque - (q) $[M][L^2][T^{-2}]$
(ii) Angular momentum - (p) $[M][L^2][T^{-1}]$
(iii) Latent heat - (s) $[M^0][L^0][T^0]$
(iv) Surface tension - (r) $[M^0][L^1][T^{-2}]$
(v) Light year - (t) $[M^0][L^1][T^0]$
Therefore, the correct matching is (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r), (v)-(t), which corresponds to Option C.
• Torque (i): Dimensions are $[M][L^2][T^{-2}]$ which corresponds to angular momentum.
• Angular momentum (ii): Dimensions are $[M][L^2][T^{-1}]$.
• Latent heat (iii): Dimensions are $[M^0][L^0][T^{-2}]$, which corresponds to energy per unit mass, typically measured in Joules per kg ($J/kg$).
• Surface tension (iv): Dimensions are $[M^0][L^1][T^{-2}]$, equivalent to force per unit length.
• Light year (v): This is a measure of distance and has dimensions $[M^0][L^1][T^0]$.
Step 2: Match these dimensions with Column-II:
(i) Torque - (q) $[M][L^2][T^{-2}]$
(ii) Angular momentum - (p) $[M][L^2][T^{-1}]$
(iii) Latent heat - (s) $[M^0][L^0][T^0]$
(iv) Surface tension - (r) $[M^0][L^1][T^{-2}]$
(v) Light year - (t) $[M^0][L^1][T^0]$
Therefore, the correct matching is (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r), (v)-(t), which corresponds to Option C.
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