Match the physical constants in List I with their dimensions in List II. List I: A. Boltzmann constant, B. Stefan constant, C. Planck constant, D. Gravitational constant. List II: I. [M⁻¹ L³ T⁻²], II. [M L² T⁻¹], III. [M L² T⁻² K⁻¹], IV. [M T⁻³ K⁻⁴]. Choose the correct matching.
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Question

Match the physical constants in List I with their dimensions in List II. List I: A. Boltzmann constant, B. Stefan constant, C. Planck constant, D. Gravitational constant. List II: I. [M⁻¹ L³ T⁻²], II. [M L² T⁻¹], III. [M L² T⁻² K⁻¹], IV. [M T⁻³ K⁻⁴]. Choose the correct matching.

Options

G1 Physics · Accepted Answer

Boltzmann constant has dimensions of energy per temperature: [k] = M L² T⁻² K⁻¹, so A → III. From Stefan's law, P ÷ A = σT⁴. Therefore, [σ] = M T⁻³ K⁻⁴, so B → IV. Planck constant has dimensions [h] = M L² T⁻¹, so C → II. From Newton's law of gravitation, F = Gm₁m₂ ÷ r². Therefore, [G] = M⁻¹ L³ T⁻², so D → I. Hence the correct matching is A → III, B → IV, C → II, D → I. Correct option: C.