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Calculate the energy stored in a wire with length 4 m, cross-sectional area 3e-6 m2, extension 1 mm, and Young's Modulus 2e11 Pa.

Physics

ScanSolve AI Answer

Answer

C

Step-by-step solution

3 steps

To calculate the energy stored in the wire, we use the formula for elastic potential energy.

  1. Identify the given values and the formula.

    Given:
    Length of wire, l=4 ml = 4 \text{ m}
    Cross-sectional area, A=3×10−6 m2A = 3 \times 10^{-6} \text{ m}^2
    Extension, e=1 mm=1×10−3 me = 1 \text{ mm} = 1 \times 10^{-3} \text{ m}
    Young's Modulus, E=2×1011 PaE = 2 \times 10^{11} \text{ Pa}

    The energy stored (elastic potential energy) in a stretched wire is given by the formula:

    U=12EAe2lU = \frac{1}{2} \frac{E A e^2}{l}
  2. Substitute the given values into the formula.

    U=12(2×1011 Pa)×(3×10−6 m2)×(1×10−3 m)24 mU = \frac{1}{2} \frac{(2 \times 10^{11} \text{ Pa}) \times (3 \times 10^{-6} \text{ m}^2) \times (1 \times 10^{-3} \text{ m})^2}{4 \text{ m}}
  3. Perform the calculation.

    U=12(2×1011)×(3×10−6)×(1×10−6)4U = \frac{1}{2} \frac{(2 \times 10^{11}) \times (3 \times 10^{-6}) \times (1 \times 10^{-6})}{4} U=2×3×1011−6−62×4U = \frac{2 \times 3 \times 10^{11 - 6 - 6}}{2 \times 4} U=6×10−18U = \frac{6 \times 10^{-1}}{8} U=0.68U = \frac{0.6}{8} U=0.075 JU = 0.075 \text{ J}

    The energy stored in the wire is 0.075 J0.075 \text{ J}.

    Comparing this with the given options:
    A. 0.053J
    B. 0.15J
    C. 0.075J
    D. 0.0075J

    The correct option is C.

    The final answer is C. 0.075J\boxed{\text{C. } \textbf{0.075J}}

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