|Class 11 Physics Units and Measurements||Applications of Dimensional Analysis|
Applications of Dimensional Analysis
Checking Dimensional Consistency of equations
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
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