Q.26. Match List-I with List-II.
List-I List-II
(A) Meter (L) I.
(B) Second (S) II.
(C) Kilogram (

Q: What is the correct answer for JEE Main Physics Q26?

The correct answer is 2. Sol. The dimensions of the fundamental constants are: [h] = [ML²T⁻¹] (Planck's constant) [G] = [M⁻¹L³T⁻²] (Gravitational constant) [c] = [LT⁻¹] (Speed of light) [K] = [K] (Kelvin, for temperature) Let's find the dimensions of the expressions in List-II: I. $\sqrt{\frac{hc}{VG}}$: This expression is not standard. The OCR solution uses $\sqrt{\frac{hG}{c^3}}$ for (A) and $\sqrt{\frac{Gh}{c^5}}$ for

Q: Q.26. Match List-I with List-II. List-I List-II (A) Meter (L) I. (B) Second (S) II. (C) Kilogram (M) III. (D) Kelvin (K) IV. where h (Planck's constant), G (gravitational constant) and c (speed…

The correct answer is 2. Sol. The dimensions of the fundamental constants are: [h] = [ML²T⁻¹] (Planck's constant) [G] = [M⁻¹L³T⁻²] (Gravitational constant) [c] = [LT⁻¹] (Speed of light) [K] = [K] (Kelvin, for temperature) Let's find the dimensions of the expressions in List-II: I. $\sqrt{\frac{hc}{VG}}$: This expression is not standard. The OCR solution uses $\sqrt{\frac{hG}{c^3}}$ for (A) and $\sqrt{\frac{Gh}{c^5}}$ for

Q: What are the options for this JEE Main Physics question?

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

Question

Q.26. Match List-I with List-II.
List-I List-II
(A) Meter (L) I. 
(B) Second (S) II. 
(C) Kilogram (M) III. 
(D) Kelvin (K) IV. 
where h (Planck's constant), G (gravitational constant) and c (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below:
(1) A-II, B-IV, C-I, D-III
(2) A-IV, B-II, C-I, D-III
(3) A-IV, B-I, C-II, D-III
(4) A-III, B-I, C-II, D-IV

FirstInTest · Accepted Answer

Sol. The dimensions of the fundamental constants are:
[h] = [ML²T⁻¹] (Planck's constant)
[G] = [M⁻¹L³T⁻²] (Gravitational constant)
[c] = [LT⁻¹] (Speed of light)
[K] = [K] (Kelvin, for temperature)

Let's find the dimensions of the expressions in List-II:
I. $\sqrt{\frac{hc}{VG}}$: This expression is not standard. The OCR solution uses $\sqrt{\frac{hG}{c^3}}$ for (A) and $\sqrt{\frac{Gh}{c^5}}$ for (B). Let's re-evaluate based on standard Planck units or similar derivations.

Let's check the options given in the OCR solution for each quantity:
(A) Meter (L):
Option IV: $\sqrt{\frac{Gh}{c^3}}$
$[\sqrt{\frac{Gh}{c^3}}] = [\sqrt{\frac{(M^{-1}L^3T^{-2})(ML^2T^{-1})}{(LT^{-1})^3}}] = [\sqrt{\frac{L^5T^{-3}}{L^3T^{-3}}}] = [\sqrt{L^2}] = [L]$. So, A-IV.

(B) Second (S):
Option II: $\sqrt{\frac{Gh}{c^5}}$
$[\sqrt{\frac{Gh}{c^5}}] = [\sqrt{\frac{(M^{-1}L^3T^{-2})(ML^2T^{-1})}{(LT^{-1})^5}}] = [\sqrt{\frac{L^5T^{-3}}{L^5T^{-5}}}] = [\sqrt{T^2}] = [T]$. So, B-II.

(C) Kilogram (M):
Option I: $\sqrt{\frac{hc}{VG}}$ (This is a typo in the question, it should be $\sqrt{\frac{hc}{G}}$ for mass)
Let's use the OCR's solution for C-I: $\sqrt{\frac{hc}{G}}$
$[\sqrt{\frac{hc}{G}}] = [\sqrt{\frac{(ML^2T^{-1})(LT^{-1})}{M^{-1}L^3T^{-2}}}] = [\sqrt{\frac{ML^3T^{-2}}{M^{-1}L^3T^{-2}}}] = [\sqrt{M^2}] = [M]$. So, C-I.

(D) Kelvin (K):
Option III: $\sqrt{\frac{K^2L^2c^3}{Gh}}$ (This is also a typo in the question, it should be related to temperature)
Let's use the OCR's solution for D-III: $\frac{K^2L^2c^3}{Gh}$ is not a standard dimension for K.
The OCR solution shows: $[K] = [K]$. The expression for Kelvin is usually related to Boltzmann constant. The given options for D are not standard. Let's look at the given options for the question.
Option (2) is A-IV, B-II, C-I, D-III.
If C-I is $\sqrt{\frac{hc}{G}}$, then it matches M.
If D-III is $\sqrt{\frac{K^2L^2c^3}{Gh}}$, this is not a standard dimension for K. However, the question states 'K' as Kelvin, and the expression in List-II is given as $\frac{K^2L^2c^3}{Gh}$. Let's assume K in the expression refers to some constant, not Kelvin. But the question explicitly states 'K' as Kelvin.

Let's re-examine the question's List-II entries exactly as written:
I. $\sqrt{\frac{hc}{VG}}$ (This 'V' is problematic. It's likely a typo for 'G' or 'h' or some other constant, or it's a completely different expression.) The OCR solution uses $\sqrt{\frac{hc}{G}}$ for C-I.
II. $\sqrt{\frac{Gh}{c^5}}$ (Matches T)
III. $\sqrt{\frac{K^2L^2c^3}{Gh}}$ (This is not a standard expression for M or K. The OCR solution uses $\sqrt{\frac{hc}{G}}$ for C-I, and for D-III it uses $\frac{K^2L^2c^3}{Gh}$ as a placeholder for K, but the actual calculation for K is not shown.)
IV. $\sqrt{\frac{Gh}{c^3}}$ (Matches L)

Given the OCR's answer (2) A-IV, B-II, C-I, D-III, let's assume the List-II entries are intended to be:
I. $\sqrt{\frac{hc}{G}}$ (for Mass)
II. $\sqrt{\frac{Gh}{c^5}}$ (for Time)
III. (Some expression for Kelvin, or the given expression is meant to be for Kelvin)
IV. $\sqrt{\frac{Gh}{c^3}}$ (for Length)

So, A (L) $\rightarrow$ IV ($\sqrt{\frac{Gh}{c^3}}$)
B (S) $\rightarrow$ II ($\sqrt{\frac{Gh}{c^5}}$)
C (M) $\rightarrow$ I ($\sqrt{\frac{hc}{G}}$) (assuming the typo in the question for I is corrected)
D (K) $\rightarrow$ III (The expression $\sqrt{\frac{K^2L^2c^3}{Gh}}$ is dimensionally incorrect for Kelvin. However, if we assume 'K' in the expression $\sqrt{\frac{K^2L^2c^3}{Gh}}$ is a constant with dimensions of temperature, then it would be [K]. But the question asks to match Kelvin. This is a problematic part of the question. Given the provided answer, we have to assume D-III is the correct match for Kelvin, despite the dimensional inconsistency of the expression itself if K is Kelvin.)

Let's check the OCR's detailed solution for D-III. It just states that the expression for K is $\frac{K^2L^2c^3}{Gh}$ and doesn't show a dimensional analysis for it. This confirms the ambiguity. However, since the other three match perfectly, and D-III is the only remaining option, it must be the intended match.

Final mapping based on OCR's answer:
A $\rightarrow$ IV
B $\rightarrow$ II
C $\rightarrow$ I
D $\rightarrow$ III

Answer

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

Answer

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

Answer

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

Answer

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

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