JEE Main · PhysicsHard

$The frequency of vibration of a string depends on length l, tension T, and mass per unit length m . Using dimensional analysis, the correct relation is?$

Show correct answer & step-by-step solution

Correct answer: A — $f \propto \frac{1}{l} \frac{T}{m}$

Solution

Dimensions: [f] = [T^{- 1}], [l] = [L], [T] = [M L T^{- 2}], [m] = [M L^{- 1}] . The ratio \frac{T}{m} has dimensions \frac{M L T ^{- 2}}{M L ^{- 1}} = [L^{2} T^{- 2}] . Thus, \frac{T}{m} has dimensions [L T^{- 1}] . Dividing by [L] gives [T^{- 1}], which matches frequency.