In an investigation to find the Young modulus $E$ of the material in a wire, the measurements recorded are shown below. Mass suspended from the wire end: $m = 2.300 \pm 0.002\,\text{kg}$ Initial length of wire: $l = 2.864 \pm 0.005\,\text{m}$ Wire diameter: $d = 0.82 \pm 0.01\,\text{mm}$ Wire extension: $e = 7.6 \pm 0.2\,\text{mm}$ The Young modulus is found from $E = \dfrac{4mgl}{\pi d^2 e}$ where $g$ represents the acceleration of free fall. The obtained value of $E$ is $1.61 \times 10^{10}\,\text{N m}^{-2}$. In what form should the value of $E$ and its uncertainty be written?
- A$(1.61 \pm 0.04) \times 10^{10}\,\text{N m}^{-2}$
- B$(1.61 \pm 0.05) \times 10^{10}\,\text{N m}^{-2}$
- C$(1.61 \pm 0.07) \times 10^{10}\,\text{N m}^{-2}$
- D$(1.61 \pm 0.09) \times 10^{10}\,\text{N m}^{-2}$