Class 11 Physics Units and Measurements Applications of Dimensional Analysis

Applications of Dimensional Analysis

Checking Dimensional Consistency of equations

• A dimensionally correct equation must have same dimensions on both sides of the equation.
• A dimensionally correct equation need not be a correct equation but a dimensionally incorrect equation is always wrong. It can test dimensional validity but not find exact relationship between the physical quantities.

Example, x = x0 + v0t + (1/2) at2Or Dimensionally, [L] = [L] + [LT-1][T] + [LT-2][T2]

x – Distance travelled in time t, x0 – starting position, v0 - initial velocity, a – uniform acceleration.

Dimensions on both sides will be [L] as [T] gets cancelled out. Hence this is dimensionally correct equation.

Deducing relation among physical quantities

• To deduce relation among physical quantities, we should know the dependence of one quantity over others (or independent variables) and consider it as product type of dependence.
• Dimensionless constants cannot be obtained using this method.

Example, T = k lxgymz

Or [L0M0T1] = [L1]x [L1T-2]y [M1]z= [Lx+yT-2y Mz]

Means, x+y = 0, -2y = 1 and z = 0. So, x = ½, y = -½ and z = 0

So the original equation reduces to T = k √l/g

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