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 \underline\hspace2cm\times 10 ^-6 m. [Young's modulus for steel = 2 \times 10 ^11 Nm ^-2 and g = 10 ms ^-2 ]

Properties of Matter PYQ — JEE Main 2023 · 10 Apr · Shift 1 · Q74 with Solution

View written solutionFree

Correct answer: 20

For a wire of length $L$ , cross-sectional area $A$ , under tension $T$ , elongation is

\Delta L = \frac{TL}{AY}

where $Y$ is Young's modulus.

From the given loading arrangement, the steel wire supports a load of $10\,\text{kg}$ .

So,

T = mg = 10 \times 10 = 100\,\text{N}

Given radius:

r = 0.2\,\text{cm} = 0.002\,\text{m}

Cross-sectional area:

A = \pi r^2 = \pi (0.002)^2 = 4\pi \times 10^{-6}\,\text{m}^2

Using $Y_{\text{steel}} = 2 \times 10^{11}\,\text{N/m}^2$ and from the figure, length of steel wire $L = 0.5\,\text{m}$ :

\Delta L = \frac{100 \times 0.5}{(4\pi \times 10^{-6})(2 \times 10^{11})}

= \frac{50}{8\pi \times 10^5}

\approx 2 \times 10^{-5}\,\text{m}

= 20 \times 10^{-6}\,\text{m}

The elongation of the steel wire is

\boxed{20 \times 10^{-6}\,\text{m}}

So the required integer is:

\boxed{20}