Which of the following units denotes the dimensions [ML^2 / Q^2], where Q denotes the electric c

step 1 Hello students in this question which of the following quantity represent the dimension of m l2

Which of the following units denotes the dimensions [ML^2 /...

Which of the following units denotes the dimensions $\left[\mathrm{ML}^{2} / Q^{2}\right]$, where $Q$ denotes the electric charge? [AIEEE 2006]
(a) Henry
(b) $\mathrm{Hm}^{-2}$
(c) Weber (Wb)
(d) $\mathrm{Wbm}^{-2}$

Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used in physics to ensure that equations are physically consistent by comparing the dimensions (such as mass [M], length [L], time [T], and electric charge [Q]) on both sides of an equation. This method helps in deducing or verifying the relationships between different physical quantities and in converting units to their equivalent expressions.

Inductance

Inductance is a property of electrical circuits that quantifies the ability of a conductor to induce an emf (electromotive force) when the current flowing through it changes. In the SI system, the unit of inductance is the Henry (H), which has derived dimensions that can be expressed in terms of the fundamental quantities, specifically [ML²/T²I²]. With the relation I = Q/T, it is equivalently represented as [ML²/Q²].

SI Units and Derived Dimensions

The International System of Units (SI) provides a standardized framework for measuring physical quantities using base units such as mass, length, time, and electric charge. Derived units, like those for inductance, are obtained by combining these base units in accordance with the physical laws governing the phenomena. Understanding these derived dimensions is crucial in fields like electromagnetism where various units interact and are interconverted based on their underlying fundamental dimensions.

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