Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemipshere $(x^2+y^2+z^2=1; \: z \geq 0)$, the value of integral $ \int (\nabla \times \overrightarrow{u}) \bullet \hat{n} \: dS$ evaluated on the curved surface of the hemishepre $S$ is
- $- \dfrac{\pi}{2} \\$
- $\dfrac{\pi}{3} \\$
- $\dfrac{\pi}{2} \\$
- $\pi$