$A$ student performs an experiment to determine the Young's modulus of a wire of length $2 \, m$ using Searle's method. In an observation,for a load of $10 \, kg$,the extension of the wire is measured as $0.88 \, mm$ with an uncertainty of $\pm 0.05 \, mm$. The student also measures the diameter of the wire as $0.4 \, mm$ with an uncertainty of $\pm 0.01 \, mm$. Take $g = 9.8 \, m/s^2$ (exact). Calculate the Young's modulus of the wire.

• A
  $(2.0 \pm 0.3) \times 10^{11} \, N/m^2$
• B
  $(2.0 \pm 0.2) \times 10^{11} \, N/m^2$
• C
  $(2.0 \pm 0.1) \times 10^{11} \, N/m^2$
• D
  $(2.0 \pm 0.05) \times 10^{11} \, N/m^2$