Two wires each of radius 0.2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is _______ $$\times 10^{-6}$$ m. [Young's modulus for steel $$= 2 \times 10^{11}$$ N m$$^{-2}$$ and $$g = 10$$ m s$$^{-2}$$]

The steel wire is the upper wire, meaning it supports the combined weight of both hanging masses ($$2 \text{ kg}$$ and $$1.14 \text{ kg}$$):

$$F = (m_1 + m_2)g$$

$$F = (2 + 1.14) \times 10 = 31.4 \text{ N}$$

The radius is $$0.2 \text{ cm} = 2 \times 10^{-3} \text{ m}$$:

$$A = \pi r^2 = \pi \times (2 \times 10^{-3})^2 = 4\pi \times 10^{-6} \text{ m}^2$$

$$\Delta L = \frac{FL}{AY}$$: $$\Delta L = \frac{31.4 \times 1.6}{(4\pi \times 10^{-6}) \times (2 \times 10^{11})}$$

$$\Delta L = \frac{50.24}{8\pi \times 10^5}$$

$$2 \times 10^{-5} \text{ m} = 20 \times 10^{-6} \text{ m}$$

The value is 20.