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Physics Question 26 – JEE-MAIN 2026

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Match List - I with List - II. List - IList - IIA. Meter (L)I. hcGB. Second (S)II. Ghc5C. Kilogram (M)III. k2L2c3GhD. Kelvin (K)IV. Ghc3 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 :

The problem requires expressing fundamental physical quantities (Length, Time, Mass, Temperature) in terms of given fundamental constants (h, G, c) using their dimensions.

Step 1: Determine Dimensions of Fundamental Constants✦ Active

The dimensions of the given fundamental constants are:

h (Planck's constant)=[ML2T−1] G (Gravitational constant)=[M−1L3T−2] c (Speed of light)=[LT−1]
Step 2: Calculate Dimensions for Each Expression in List-II○ Expand

We calculate the dimensions for each expression in List-II:

I. hcG=[ML2T−1][LT−1][M−1L3T−2]=[ML3T−2][M−1L3T−2]=[M2]=[M] II. Ghc5=[M−1L3T−2][ML2T−1][LT−1]5=[L5T−3][L5T−5]=[T2]=[T] IV. Ghc3=[M−1L3T−2][ML2T−1][LT−1]3=[L5T−3][L3T−3]=[L2]=[L]
💡 Teacher's Secret Hint

Be careful with exponent calculations, especially when dealing with negative exponents and fractions.

Step 3: Match List-I with List-II and Select the Correct Option○ Expand

Based on the dimensional analysis:

A. Meter (L)→IV. [L] B. Second (S)→II. [T] C. Kilogram (M)→I. [M]

By elimination, D. Kelvin (K) must match III. Comparing these matches with the given options, Option 2 (A-IV, B-II, C-I, D-III) is the correct answer.

💡 Teacher's Secret Hint

Even if one expression seems ambiguous, often the other clear matches can lead to the correct option by elimination in multiple-choice questions.

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