\(g_{T}\) greatest where \(x_o\) is small resulting in high curvature.
For the case of a sphere,
\(g^2_{net}=g_Tsin^2(\theta)+(g_Tcos(\theta)-g)^2\)
If we let,
\(2g_{net}\cfrac{\partial g_{net}}{\partial\theta}=2g_Tsin(\theta)cos(\theta)-2(g_Tcos(\theta)-g)sin(\theta)=0\)
\(2gsin(\theta)=0\)
\(\theta\) = 0o or 90o
Now consider,
\(2(\cfrac{\partial g_{net}}{\partial\theta})^2+2g_{net}\cfrac{\partial^2 g_{net}}{\partial\theta^2}=2gcos(\theta)\)
when \(\theta\) = 0 o
\(\cfrac{\partial^2 g_{net}}{\partial\theta^2}>0\)
We know that at 0o, \(g_{net}\) is a minimum from \(\cfrac{\partial^2 g_{net}}{\partial\theta^2}\)
This means, forces at the side of the surface beyond 0o to the central line are pulling the outwards with higher strength. This force distribution tends to open the top of the heated body where \(g_{net}\) is minimum.
