Find the pendulum's formula from dimensions alone
"Find the pendulum's formula from dimensions alone" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Deducing relations by dimensions" in Units and Measurements. Slide the powers of l and g. The ledger compares the dimensions of both sides; mass appears only in m, so its power must be 0. Dimensions fix the powers, T ∝ √(l/g), and show the mass drops out. They can never give the number 2π. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Deducing relations by dimensions in Units and Measurements. Change the values and watch what happens.
In JEE Main
42 shifts analysed
61 questions from Units and Measurements across the 42 JEE Main shifts Lumi has analysed (2017–2026).
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.
Questions
3 answers
- What does the "Find the pendulum's formula from dimensions alone" simulation show?
- Slide the powers of l and g. The ledger compares the dimensions of both sides; mass appears only in m, so its power must be 0.
- Does JEE Main ask questions from Units and Measurements?
- Yes. JEE Main asked 61 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Deducing relations by dimensions" in Units and Measurements (Class 11 Physics).
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