Question

A sonometer wire having cross sectional area 0.85×1/1000000 m2 is stretched between two rigid supports 1.2 my apart .A tension of 20 N is applied at its free end .if the temperature is reduced by 12°C, Calculate the field tension in the wire .Take coefficient of linear expansion & isothermal young's modulus to be 1.5× 1/100000 1/K & 2 ×100000000000 N/my, respectively.

Answer 1

Answer on Question #66753-Physics-Molecular Physics-Thermodynamics

A sonometer wire having cross sectional area $0.85 \times 1/1000000 \, \text{m}^2$ is stretched between two rigid supports $1.2 \, \text{my}$ apart. A tension of $20 \, \text{N}$ is applied at its free end. If the temperature is reduced by $12{}^{\circ} \text{C}$ , Calculate the field tension in the wire. Take coefficient of linear expansion & isothermal young's modulus to be $1.5 \times 1/100000 \, \text{N} / \text{K}$ & $2 \times 100000000000 \, \text{N} / \text{my}$ , respectively.

Solution

$$\Delta F = - A \gamma \alpha \Delta T$$ $$\Delta F = (0. 8 5 \cdot 1 0 ^ {- 6}) (2 \cdot 1 0 ^ {1 1}) (1. 5 \cdot 1 0 ^ {- 5}) (1 2) =$$ $$F ^ {\prime} = F + \Delta F = 2 0 + 3 0. 6 = 5 0. 6 N.$$

Answer: 50.6 N.

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