Question

A wire of cross-sectional area \( 10^{-6} \, m^2 \) is elongated by \( 0.1 \% \) when the tension in it is \( 1000 \, N \). The Young's modulus of the material of the wire is (Assume radius of the wire is constant)?

• A. \( 10^{11} \, Nm^{-2} \)
• B. \( 10^{12} \, Nm^{-2} \)
• C. \( 10^{10} \, Nm^{-2} \)
• D. \( 10^{9} \, Nm^{-2} \)

Hint:

Young's modulus measures the stiffness of a material. It is calculated using the ratio of stress to strain, ensuring units are correctly converted for accurate results.

Answer 1

The Correct Option is B

The Young's modulus (\( Y \)) is given by the formula: \[ Y = \frac{\text{Stress}}{\text{Strain}} \] 

Step 1: Calculate Stress 
Stress is defined as force per unit area: \[ \text{Stress} = \frac{F}{A} \] Given: \[ F = 1000 \, N, \quad A = 10^{-6} \, m^2 \] \[ \text{Stress} = \frac{1000}{10^{-6}} \] \[ = 10^9 \, Nm^{-2} \] 

Step 2: Calculate Strain 
Strain is given as the ratio of change in length to the original length: \[ \text{Strain} = \frac{\Delta L}{L} \] Given \( \frac{\Delta L}{L} = 0.1\% = \frac{0.1}{100} = 10^{-3} \), 

Step 3: Compute Young's modulus 
\[ Y = \frac{10^9}{10^{-3}} \] \[ = 10^{12} \, Nm^{-2} \] Thus, the Young's modulus of the material is \( 10^{12} \, Nm^{-2} \).