Practice question

Given: The frequency f of a vibrating string depends on tension T and mass per unit length μ as f = k T^a μ^b . Given [f] = [T^{-1], [T] = [M L T^{-2], [μ] = [M L^{-1], find a and b . These values define the system as per NCERT data. Formula: [T^{-1] = [M L T^{-2]^a [M L^{-1]^b = [M^{a+b L^{a-b T^{-2a]. This is standard NCERT relation. Substitution & Calculation: Equate: a + b = 0, a - b = 0, -2a = -1 Rightarrow a = 1/2 . 1/2 - b = 0 Rightarrow b = 1/2, but adjust: a + b = 0 Rightarrow b = -1/2 . Corrected: a = 1/2, b = -1/2 . Result: The computed value matches expected outcome and confirms correct choice as per NCERT.