Question

Match the column

• A. A \( \rightarrow \) R; B \( \rightarrow \) P; C \( \rightarrow \) S; D \( \rightarrow \) S
• B. A \( \rightarrow \) T; B \( \rightarrow \) P; C \( \rightarrow \) U; D \( \rightarrow \) S
• C. A \( \rightarrow \) R; B \( \rightarrow \) T; C \( \rightarrow \) Q; D \( \rightarrow \) Q
• D. A \( \rightarrow \) T; B \( \rightarrow \) U; C \( \rightarrow \) S; D \( \rightarrow \) Q

Hint:

Ensure that the dimensions of physical quantities are checked thoroughly when matching terms in dimensional analysis.

Answer 1

The Correct Option is A

To solve this problem, we need to match the physical quantities in Column-I with their corresponding dimensional formulas in Column-II.

1. Thermal Conductivity (A):
   The dimensional formula for thermal conductivity is [MLT^{-3}K^{-1}]. It represents how heat is conducted through a material per unit time, per unit area, per unit temperature gradient.
2. Boltzmann Constant (B):
   The dimensional formula for the Boltzmann constant is [ML^2T^{-2}]. This constant relates the average kinetic energy of particles in a gas with the temperature of the gas.
3. Spring Constant (C):
   The dimensional formula for the spring constant is [MLT^{-2}]. It describes the stiffness of a spring by quantifying the force needed per unit extension or compression.
4. Surface Tension (D):
   The dimensional formula for surface tension is [MLT^{-2}]. Surface tension is the force per unit length acting along a line in the surface of a liquid.

Based on the above explanations, we can match as follows:

• A \( \rightarrow \) R: Thermal Conductivity \( \rightarrow [MLT^{-3}K^{-1}] \)
• B \( \rightarrow \) P: Boltzmann Constant \( \rightarrow [ML^2T^{-2}] \)
• C \( \rightarrow \) S: Spring Constant \( \rightarrow [MLT^{-2}] \)
• D \( \rightarrow \) S: Surface Tension \( \rightarrow [MLT^{-2}] \)

Thus, the correct answer is: A \( \rightarrow \) R; B \( \rightarrow \) P; C \( \rightarrow \) S; D \( \rightarrow \) S.