Simulation · Physics · Class 11

Find the pendulum's formula from dimensions alone

From the lesson Deducing relations by dimensions in Units and Measurements. Change the values and watch what happens.

The idea behind it

NCERT §1.6.2

If you know which quantities (up to three independent ones) a result depends on, assume it is a product of their powers and match dimensions to find the powers.
For a simple pendulum take T = k lˣ gʸ mᶻ. Matching [T] = [L]ˣ [L T⁻²]ʸ [M]ᶻ gives x + y = 0, −2y = 1 and z = 0.
So x = ½, y = −½, z = 0 and T = k√(l/g): the period does not depend on the mass of the bob.
The dimensionless constant k cannot come from dimensions; experiment or theory gives k = 2π, so T = 2π√(l/g).
The method fails to give dimensionless constants, cannot tell apart quantities with the same dimensions (work and torque, for example), and cannot handle sums of terms or trigonometric, logarithmic and exponential dependence.

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