FAQ on Dimensional Analysis

Dimensional analysis

The dimensional analysis comes under the topic Units and Dimension in physics. Having a good hold on this chapter helps you to eliminate options in multiple choice questions which can be very handy. Some of the FAQ’s related to this topics are discussed below.

1) What is the meaning of dimension in physics?

Ans – It is an expression that relates derived quantity to fundamental quantities. But it is not related to the magnitude of the derived quantity.

2) What is the dimension of force?

Ans – We know, \(F\) = \(ma\) —– (1)

Mass is fundamental quantity but acceleration is a derived quantity and can be represented in terms of fundamental quantities.

\(a\) = \([LT^{-2}]\) —– (2)

Using (1) and (2),

\(F\) = \([M LT^{-2}]\)

This is the dimension of force.

3) What is dimensional analysis?

Ans – Dimensional analysis is based on the principle that two quantities having same dimensions can only be compared with one another. For example, I can compare kinetic energy with potential energy and say they equal or one is greater than another because they have the same dimension. But I cannot kinetic energy with force or acceleration as their dimensions are not same.

4) How to do demonstrate dimensional analysis with an example?

Ans – Suppose I have the following equation,

\(F\) = \(E^a~ . ~V^b~ .~ T^c\)

Where, \(F\) = Force; \(E\) = Energy; \(V\) = Velocity; \(M\) = Mass

We need to find the value of \(a\), \(b\) and \(c\).

Following are the dimensions of the given quantities,

\(F\) = \([MLT^{-2}]\), \(E\) = \([ML^2T^{-2}]\), \(V\) = \([LT^{-1}]\)

According to dimensional analysis the dimension of RHS should be equal to LHS hence,

\([MLT^{-2}]\) = \([ML^2T^{-2}]^a~ . ~[LT-1]^b~ . ~[T]^c\)

\([MLT^{-2}]\) = \([M^a~ L^{2a+b}~ T^{-2a-b+c}]\)

Now we have three equations,

\(a\) = \(1\)

\(2a+b\) = \(1\)

\(-2a~-~b~+~c\) = \(-2\)

Solving the three equations we get,

\(a\) = \(1\), \(b\) = \(-1\) and \(c\) = \(-1\).

5) What are some of the best books to refer for unit and dimensions in physics?

Ans – When it comes to books for JEE preparation H.C. Verma is definitely one of the best books. Apart from that, books by Arihant Publication also have good dimensional analysis practice problems.

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A chemical reaction XY is said to be in equilibrium when -