Mechanical Properties of Solids

JEE Main level, single correct, medium

8 of 118

Question 8 of 118

Figure represents the extension (Δl\Delta l) of a wire of length 11 meter, suspended from the ceiling of the room at one end with a load WW connected to the other end. If the cross-sectional area of the wire is 10−510^{-5} m2^2 then the Young's modulus of the wire is __________ N/m2^2.

Show answer and solution

Answer: (C) 1.0×10101.0 \times 10^{10}

From the given graph, we can observe that for a load W=20W = 20 N, the extension is Δl=2×10−4\Delta l = 2 \times 10^{-4} m.

The formula for Young's modulus
YY is:

Y=StressStrain=W/AΔl/L=WLAΔlY = \dfrac{\text{Stress}}{\text{Strain}} = \dfrac{W / A}{\Delta l / L} = \dfrac{W L}{A \Delta l}

Given:

Length of the wire,
L=1L = 1 m
Cross-sectional area,
A=10−5A = 10^{-5} m2^2

Substituting the values into the formula:


Y=20×110−5×2×10−4Y = \dfrac{20 \times 1}{10^{-5} \times 2 \times 10^{-4}}

Y=202×10−9Y = \dfrac{20}{2 \times 10^{-9}}

Y=10×109=1.0×1010Y = 10 \times 10^9 = 1.0 \times 10^{10} N/m2^2

Answer:
1.0×10101.0 \times 10^{10}

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