The dimensions of angular momentum, latent heat and capacitance are, respectively.
- $ML^2T^1A^2, L^2T^{-2}, M^{-2}L^{-2}T^2$
- $ML^2T^{-1}, L^2T^{-2}, M^{-1}L^{-2}T^4A$
- $ML^2T^{-2}, L^2T^{-2}, ML^{2}TA^2$
- $ML^2T^{-1}, L^2T^{-2}, M^{-1}L^{-2}T^4A^2$
The Correct Option is D
Solution and Explanation
Top Questions on Dimensional Analysis
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:
- JEE Advanced - 2025
- Physics
- Dimensional Analysis
A quantity \( X \) is given by: \[ X = \frac{\epsilon_0 L \Delta V}{\Delta t} \] where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( L \) is the length,
- \( \Delta V \) is the potential difference,
- \( \Delta t \) is the time interval.
The dimension of \( X \) is the same as that of:- WBJEE - 2025
- Physics
- Dimensional Analysis
- The dimensions of \( (\mu \epsilon)^{-1} \), where \( \epsilon \) is permittivity and \( \mu \) is permeability of a medium, are:
- CBSE CLASS XII - 2025
- Physics
- Dimensional Analysis
- The dimensional formula of magnetic permeability \(\mu_0\) is:
- CBSE CLASS XII - 2025
- Physics
- Dimensional Analysis
- If the equation for the velocity of a particle at time 't' is \(v = at + \frac{b}{t+c}\), then the dimensions of a, b, c are respectively
- AP EAPCET - 2025
- Physics
- Dimensional Analysis
Questions Asked in JEE Main exam
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
- JEE Main - 2025
- System of Particles & Rotational Motion
Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is ….. (Nearest integer).
- JEE Main - 2025
- Electrolysis
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
- JEE Main - 2025
- Calculus
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
- Arrange the following in increasing order of solubility product: \[ {Ca(OH)}_2, {AgBr}, {PbS}, {HgS} \]
- JEE Main - 2025
- Solutions
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.