Match List I with List II: Choose the correct answer from the options given below:

Given: Match physical quantities in List I with their dimensions in List II. Find: The correct matching. Dimensions: aligned Angular speed & T^-1 Spring constant & MT^-2 Moment of inertia & ML^2 Angular momentum & ML^2T^-1 aligned Therefore, A II, B I, C IV, D III So the correct option should be A. The solution concludes with D, but its working is unrelated to this question. Using the dimensional analysis shown by the question itself, the defensible answer is A.

Match List I with List II: Choose the correct answer from the opt… — Solution | JEE Physics

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Match List I with List II:

$A matching table with List I containing A. Spring constant, B. Angular speed, C. Angular momentum, D. Moment of Inertia, and List II containing I. $$T^{-1}$$, II. $$MT^{-2}$$, III. $$ML^2$$, IV. $$ML^2T^{-1}$$.$

Choose the correct answer from the options given below:

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

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Match physical quantities in List I with their dimensions in List II.

Find: The correct matching.

Dimensions:

\begin{aligned} \text{Angular speed} &\to T^{-1} \\ \text{Spring constant} &\to MT^{-2} \\ \text{Moment of inertia} &\to ML^2 \\ \text{Angular momentum} &\to ML^2T^{-1} \end{aligned}

Therefore,

A \to II, \quad B \to I, \quad C \to IV, \quad D \to III

So the correct option should be A.

The solution concludes with D, but its working is unrelated to this question. Using the dimensional analysis shown by the question itself, the defensible answer is A.

Common mistakes

Confusing angular speed with angular momentum. Angular speed has dimension $T^{-1}$ , whereas angular momentum has dimension $ML^2T^{-1}$ . Match the quantity with its defining formula first.
Assigning moment of inertia the dimension of force-related quantities. Moment of inertia is based on $mr^2$ , so its dimension is $ML^2$ , not $MT^{-2}$ . Use the mass-distance definition.
Using the incorrect dimension for spring constant. From $F = kx$ , we get $k = F/x$ , so dimension is $MT^{-2}$ . Do not forget that dividing force by length removes one power of $L$ .

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