Dimensional Analysis ApplicationsMediumQuestion 5018
Question
By dimensional analysis, the period T of a simple pendulum depends on length l and g. If T = k·lᵃ·gᵇ, then a and b are:
- Aa=1/2, b=−1/2Correct
- Ba=1, b=−1
- Ca=−1/2, b=1/2
- Da=1/2, b=1/2
Correct answer
a=1/2, b=−1/2
Explanation
Dimensionally [T] = [L]ᵃ[LT⁻²]ᵇ gives: T¹ implies 1 = −2b, so b = −1/2; L⁰ implies 0 = a + b, so a = 1/2. Therefore T = k√(l/g).