JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement

Match List - I with List - II.
List - I List - II
A. Boltzmann constant I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant II. \([ML^2T^{-1}]\)
C. Planck's constant III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant IV. \([ML^0T^{-3}K^{-4}]\)
Choose the correct answer from the options given below :

List - I	List - II
A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant	II. \([ML^2T^{-1}]\)
C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

A A-I, B-II, C-III, D-IV
B A-IV, B-III, C-II, D-I
C A-III, B-IV, C-II, D-I
D A-II, B-I, C-IV, D-III

Verified Solution

Answer & Solution

Correct Answer

(C) A-III, B-IV, C-II, D-I

Step-by-step Solution

Detailed explanation

Boltzmann constant \(k\): \(E = k T \Rightarrow [k] = \dfrac{[ML^2T^{-2}]}{[K]} = [ML^2T^{-2}K^{-1}]\) Stefan's constant \(\sigma\): \(\dfrac{E}{At} = \sigma T^4 \Rightarrow [\sigma] = \dfrac{[ML^2T^{-2}]}{[L^2][T][K^4]} = [ML^0T^{-3}K^{-4}]\) Planck's constant \(h\):…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II.

List-I (Relation)		List-II (Law)
A.	\(\oint \overrightarrow{ E } \cdot \overrightarrow{ d } l =-\frac{ d }{ dt } \oint \overrightarrow{ B } \cdot \overrightarrow{ d a}\)	I.	Ampere's circuital law.
B.	\(\oint\) B. \(\vec{d} l=\mu_0\left(1+\epsilon_0 \frac{d \phi_E}{d t}\right)\)	II.	Faraday's laws of electromagnetic induction.
C.	\(\oint \overrightarrow{ E } . \overrightarrow{ d a}=\frac{1}{\epsilon_0} \int \rho dv\)	III.	Ampere-Maxwell law
D.	\(\oint \overrightarrow{ B } \cdot \overrightarrow{ d } l =\mu_0 I\)	IV.	Gauss's law of electrostatics

Choose the correct answer from the options given below :

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Match List - I with List - II.List - IList - IIA. Boltzmann constantI. \([M^{-1}L^3T^{-2}]\)B. Stefan's constantII. \([ML^2T^{-1}]\)C. Planck's constantIII. \([ML^2T^{-2}K^{-1}]\)D. Gravitational constantIV. \([ML^0T^{-3}K^{-4}]\)Choose the correct answer from the options given below :

Step-by-step Solution

Match List - I with List - II.
List - I List - II
A. Boltzmann constant I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant II. \([ML^2T^{-1}]\)
C. Planck's constant III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant IV. \([ML^0T^{-3}K^{-4}]\)
Choose the correct answer from the options given below :