A $0-45-90$ strain gauge rosette is mounted on an aircraft wing. The co-ordinate system is placed such that the strain gauges $\mathrm{p}, \mathrm{q}$ and r are oriented at angles $0^{\circ}, 45^{\circ}$ and $90^{\circ}$, respectively, from the $x$ axis $\text{(see figure)}$. The strain readings associated to $\mathrm{p}, \mathrm{q}$ and r are denoted by $\varepsilon_{p}, \varepsilon_{q}$, and $\varepsilon_{r}$, respectively. While conducting a test the strain gauges show the following readings.
\[
\varepsilon_{p}=150 \times 10^{-6}, \varepsilon_{q}=180 \times 10^{-6}, \varepsilon_{r}=-90 \times 10^{-6}
\]
The developed engineering shear strain $\gamma_{x y}$ associated to the strain gauge data is
- $120 \times 10^{-6}$
- $180 \times 10^{-6}$
- $300 \times 10^{-6}$
- $240 \times 10^{-6}$
