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

• 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
  $(2.0 \pm 0.05) \times 10^{11} \,N/m^2$