Question Detail
Question
If the speed v of a wave depends on tension T (force) and mass per unit length μ, then by dimensional analysis, v is proportional to
Correct Answer
Option B is the correct answer.
Detailed Explanation
Let v ∝ Tˣ μʸ. [v] = LT⁻¹, [T] (tension, a force) = MLT⁻², [μ] (mass per unit length) = ML⁻¹. So, LT⁻¹ = (MLT⁻²)ˣ (ML⁻¹)ʸ = Mˣ⁺ʸ Lˣ⁻ʸ T⁻²ˣ. Equating exponents: For M: x + y = 0; For T: -2x = -1 ⇒ x = 1/2; then y = -1/2. So v ∝ T¹/² μ⁻¹/² = √(T/μ).
Hint
Write the dimensions of tension (force) and mass per unit length. Set up the dimensional equation and solve for the exponents.