Units & Dimensions

JEE Main level, single correct, medium

21 of 149

Question 21 of 149

Match List-I with List-II.
List-IList-IIA. Meter (L)I. hcG\sqrt{\dfrac{hc}{G}}B. Second (S)II. Ghc5\sqrt{\dfrac{Gh}{c^5}}C. Kilogram (M)III. K2L2c3Gh\sqrt{\dfrac{K^2L^2c^3}{Gh}}D. Kelvin (K)IV. Ghc3\sqrt{\dfrac{Gh}{c^3}}
where hh (Planck's constant), GG (gravitational constant) and cc (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :

Show answer and solution

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

The dimensional formulas for the given fundamental constants are:
[h]=ML2T−1[h] = M L^2 T^{-1}
[c]=LT−1[c] = L T^{-1}
[G]=M−1L3T−2[G] = M^{-1} L^3 T^{-2}

Evaluating the dimensions of the expressions in List-II:

For I: hcG=(ML2T−1)(LT−1)M−1L3T−2=M2=M\sqrt{\dfrac{hc}{G}} = \sqrt{\dfrac{(M L^2 T^{-1})(L T^{-1})}{M^{-1} L^3 T^{-2}}} = \sqrt{M^2} = M (Kilogram).
Thus, C →\rightarrow I.

For II: Ghc5=(M−1L3T−2)(ML2T−1)(LT−1)5=L5T−3L5T−5=T2=T\sqrt{\dfrac{Gh}{c^5}} = \sqrt{\dfrac{(M^{-1} L^3 T^{-2})(M L^2 T^{-1})}{(L T^{-1})^5}} = \sqrt{\dfrac{L^5 T^{-3}}{L^5 T^{-5}}} = \sqrt{T^2} = T (Second).
Thus, B →\rightarrow II.

For IV: Ghc3=(M−1L3T−2)(ML2T−1)(LT−1)3=L5T−3L3T−3=L2=L\sqrt{\dfrac{Gh}{c^3}} = \sqrt{\dfrac{(M^{-1} L^3 T^{-2})(M L^2 T^{-1})}{(L T^{-1})^3}} = \sqrt{\dfrac{L^5 T^{-3}}{L^3 T^{-3}}} = \sqrt{L^2} = L (Meter).
Thus, A →\rightarrow IV.

For III: Substituting L2=Ghc3L^2 = \dfrac{Gh}{c^3} from IV into the expression gives K2L2c3Gh=K2(Ghc3)c3Gh=K2=K\sqrt{\dfrac{K^2 L^2 c^3}{Gh}} = \sqrt{K^2 \left(\dfrac{Gh}{c^3}\right) \dfrac{c^3}{Gh}} = \sqrt{K^2} = K (Kelvin).
Thus, D →\rightarrow III.

The correct matching is A-IV, B-II, C-I, D-III.

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

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Units & Dimensions (Dimensions), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.