Q118 / 150 · MHT CET 2020 (15 Oct Shift 1) · Physics

A transverse wave is travelling with velocity ' $\mathrm{V}^{\prime}$ through a metal wire of length ' $\mathrm{L}$ ' and density ' $\rho$ '. The tensile stress in the wire is

  • A
    $\mathrm{V} \rho^{2}$
  • B
    $\frac{\mathrm{v}^{2}}{\rho}$
  • C
    $\frac{\rho}{\mathrm{V}^{2}}$
  • Correct answer
    D
    $\mathrm{~V}^{2} \rho$

Solution

$\mathrm{V}=\sqrt{\frac{T}{m}}$ where $\mathrm{T}$ is the tension and $\mathrm{m}$ is mass per unit length. $\mathrm{m}=\mathrm{A} . p$ where $\mathrm{A}$ is an area of cross-section. $\therefore V=\sqrt{\frac{T}{A \rho}}$ $\therefore V^{2}=\frac{T}{A \rho}$ $\therefore \frac{T}{A}=V^{2} \rho$

Hence, the correct answer is option: 'D'.

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