Identify the pair of physical quantities which have different dimensions.
- Wave number and Rydberg’s constant
- Stress and Coefficient of elasticity
- Coercivity and Magnetisation
- Specific heat capacity and Latent heat
The Correct Option is D
Solution and Explanation
[S]=\(\frac{[c]}{[m]}\)×[ΔT]
and, L=\(\frac{Q}{m}\)
⇒ They have different dimensions
The correct option is (D): Specific heat capacity and Latent heat
Top Questions on Dimensional Analysis
Match the LIST-I with LIST-II:
Choose the correct answer from the options given below:
- JEE Main - 2026
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Match the LIST-I with LIST-II
Choose the correct answer from the options given below:- JEE Main - 2026
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A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
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Concepts Used:
Dimensional Analysis
Dimensional Analysis is a process which helps verify any formula by the using the principle of homogeneity. Basically dimensions of each term of a dimensional equation on both sides should be the same.
Limitation of Dimensional Analysis: Dimensional analysis does not check for the correctness of value of constants in an equation.
Using Dimensional Analysis to check the correctness of the equation
Let us understand this with an example:
Suppose we don’t know the correct formula relation between speed, distance and time,
We don’t know whether
(i) Speed = Distance/Time is correct or
(ii) Speed =Time/Distance.
Now, we can use dimensional analysis to check whether this equation is correct or not.
By reducing both sides of the equation in its fundamental units form, we get
(i) [L][T]-¹ = [L] / [T] (Right)
(ii) [L][T]-¹ = [T] / [L] (Wrong)
From the above example it is evident that the dimensional formula establishes the correctness of an equation.