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QJEEM23Ph55a4: JEE Main 2023 Physics - Class 11 JEEM23Ph55a4 Solution: As shown in the figure, in an experiment to determine Young's…

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45 ∘^\circ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be x×104x\times10^4 Nm −2^{-2} . The value of xx is ___________.

JEE Main 2023 (Online) 25th January Morning Shift Physics - Properties of Matter Question 89 English

Step-by-Step Verified Solution

Given, Length, L=62.8 cmL=62.8 \mathrm{~cm}

diameter, d=4 mmd=4 \mathrm{~mm}

radius, r=2 mmr=2 \mathrm{~mm}

y=x×104 N/m2y=x \times 10^4 \mathrm{~N} / \mathrm{m}^2

JEE Main 2023 (Online) 25th January Morning Shift Physics - Properties of Matter Question 89 English Explanation

According to graph, Δl/f=tan⁡45∘=1\Delta l / f=\tan 45^{\circ}=1

Y=FLA⋅ΔLY=\frac{F L}{A \cdot \Delta L}

Y=1×62.8×10−23.14×2×2×10−6=5×104 N/m2Y=\frac{1 \times 62.8 \times 10^{-2}}{3.14 \times 2 \times 2 \times 10^{-6}}=5 \times 10^4 \mathrm{~N} / \mathrm{m}^2

∴\therefore x = 5

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