A student performs an experiment to determine the Young’s modulus of a wire, exactly 2m  long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8mm  with an uncertainty of  $\pm 0.05\text{\hspace{0.17em}mm}$ at a load of exactly  1.0kg. The student also measures the diameter of the wire to be  0.4mm with an uncertainty of  $\pm 0.01\text{\hspace{0.17em}mm}$. Take $g=9.8\text{\hspace{0.17em}m}/{\text{s}}^{\text{2}}$ (exact). The Young’s modulus obtained from the reading is[ Take $\text{π}=3.14$ ]

• A

  $\left(2.0\pm 0.3\right)\times {10}^{11}\text{\hspace{0.17em}N}/{\text{m}}^{\text{2}}$

• B

  $\left(2.0\pm 0.2\right)\times {10}^{11}\text{\hspace{0.17em}N}/{\text{m}}^{\text{2}}$

• C

  $\left(2.0\pm 0.1\right)\times {10}^{11}\text{\hspace{0.17em}N}/{\text{m}}^{\text{2}}$

• D

  $\left(2.0\pm 0.05\right)\times {10}^{11}\text{\hspace{0.17em}N}/{\text{m}}^{\text{2}}$