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A wire of area of cross-section 10^(-6) ...

A wire of area of cross-section `10^(-6) m^(2)` is increased in length by 0.1 %. The tension produced is 1000 N. The Young's modulus of wire is

A

`10^(12) N//m^(2)`

B

`10^(11) N//m^(2)`

C

`10^(10) N//m^(2)`

D

`10^(9) N//m^(2)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the Young's modulus of the wire, we can follow these steps: ### Step 1: Understand the given data - Area of cross-section (A) = \(10^{-6} \, m^2\) - Increase in length (ΔL) = 0.1% of original length (L) - Tension (Force, F) = 1000 N ### Step 2: Convert the percentage increase in length to a decimal The increase in length as a decimal can be calculated as: \[ \text{Strain} = \frac{\Delta L}{L} = \frac{0.1}{100} = 0.001 \] ### Step 3: Calculate the stress in the wire Stress (σ) is defined as the force applied per unit area. It can be calculated using the formula: \[ \sigma = \frac{F}{A} \] Substituting the values: \[ \sigma = \frac{1000 \, N}{10^{-6} \, m^2} = 1000 \times 10^6 \, N/m^2 = 10^9 \, N/m^2 \] ### Step 4: Use the definition of Young's modulus Young's modulus (E) is defined as the ratio of stress to strain: \[ E = \frac{\sigma}{\text{Strain}} \] Substituting the values we calculated: \[ E = \frac{10^9 \, N/m^2}{0.001} = 10^9 \times 10^3 \, N/m^2 = 10^{12} \, N/m^2 \] ### Step 5: Conclusion The Young's modulus of the wire is: \[ E = 10^{12} \, N/m^2 \] ---
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Knowledge Check

  • A wire of area of cross section 1xx10^(-6)m^(2) and length 2 m is stretched through 0.1 xx 10^(-3)m . If the Young's modulus of a wire is 2xx10^(11)N//m^(2) , then the work done to stretch the wire will be

    A
    `0.05xx10^(-4)J`
    B
    `0.5xx10^(-4)J`
    C
    `5xx10^(-4)J`
    D
    `50xx10^(-4)J`

  • The area of cross-section of a wire is 10^(-5) m^(2) when its length is increased by 0.1% a tension of 1000N is produced. The Young's modulus of the wire will be (in Nm^(-2) )

    A
    `10^(12)`
    B
    `10^(11)`
    C
    `10^(9)`
    D
    `10^(10)`

  • A wire of length 10 m and cross-section are 10^(-6) m^(2) is stretched with a force of 20 N. If the elongation is 1 mm, the Young's modulus of material of the wire will be

    A
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    B
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    C
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    D
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