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  • A stretched rope having linear mass density <img alt="5 \times 10^{-2} \mathrm{~kg} / \mathrm{m}" src="https://entrancecorner.oncodecogs.com/gif.latex?5%20%5Ctimes%2010%5E%7B-2%7D%20%5Cmathrm%7B%7E

A stretched rope having linear mass density 5 \times 10^{-2} \mathrm{~kg} / \mathrm{m}  is under a tension of 80 \mathrm{~N}. The power that has to be supplied to the rope to generate harmonic wares at a frequency of 60 \mathrm{~Hz} and an amplitude of 6 \mathrm{~cm} is -

Option: 1

362 \omega


Option: 2

251 \omega


Option: 3

511 \omega


Option: 4

416 \omega


Answers (1)

best_answer

v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{80}{5 \times 10^{-2}}}=40 \mathrm{~m} / \mathrm{s}

\begin{aligned} P & =\frac{1}{2} \rho \omega^2 A^2 s V \\ & =\frac{1}{2} \mu(2 \pi f)^2 \mu \\ & =\frac{1}{2} \times 5 \times 10^{-2}(2 \pi \times 60)^2 \times 40 \times(0.00)^2 \\ & =511 \omega \end{aligned}

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shivangi.bhatnagar

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