Mean curvature submanifold

Question

Consider $S^{N-1}$ the unit sphere and let us focus our attention on the cap $$ G=S^{N-1}\cap\{x_N>0\} $$ with boundary $\partial G= S^{N-2}\times\{0\}$: it is quite obvious to see that $G$ is a submanifold of $S^{N-1}$. Consider $\mbox{div}_{\partial G}$ the tangential divergence on the boundary $\partial G$ and let $$ \nu= (0,-1) \in R^N\times R $$ be the outward normal field to $\partial G$ in $S^{N-1}$. How can i compute $\mbox{div}_{\partial G} \nu$? Is this related to some mean curvature value? The idea is to use this value in order to apply a divergence type formula for $\partial G$ as a subscape of $S^{N-1}$.