A uniform wire of length l and mass M is stretched between two fixed points, keeping a tension F. A sound of frequency μ is impressed on it. Then the maximum vibrational energy is existing in the wire when μ =

Question

A uniform wire of length l and mass M is stretched between two fixed points, keeping a tension F. A sound of frequency μ is impressed on it. Then the maximum vibrational energy is existing in the wire when μ =, 1 2 ML F, FL M, 2 × FM L, 1 2 F ML

MARKS App · Accepted Answer

We should check it dimensionally Let μ = K F a M b L c μ = F a M b L c = MLT 2 a M b L c M 0 L 0 T - 1 = M a + b L a + c T - 2 a a + b = 0 ⇒ b = - a a + c = 0 ⇒ c = - a - 2 a = - 1 ⇒ a = 1 2 b = - 1 2 c = - 1 2 ⇒ μ = K F 1 2 M - 1 2 L - 1 2 μ = K F ML So only option (iv) satisfies it dimensionally.

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