A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 × 10–7 m2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s–1. If the Young's modulus of the material of the wire is n × 109 Nm

Engineering

Physics

Basics of Simple Harmonic Motion

Stress Strain and Hookes Law New

Question

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross-sectional area is 4.9 × 10^–7 m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s^–1. If the Young's modulus of the material of the wire is n × 10⁹ Nm^–2, the value of n is

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$k = \frac{YA}{L}$

$ω = \sqrt{\frac{k}{m}} = \sqrt{\frac{YA}{mL}}$

$140 = \sqrt{\frac{n \times 10^{9} \times 4 .9 \times 10^{- 7}}{0 .1 \times 1}} = \sqrt{49 n \times 10^{2}}$

$140 = 70 \sqrt{n}$

n = 4