Consider regular polygons with number of sides $n=3, 4, 5, \ldots$ as shown in the figure. The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is $\Delta$. Then $\Delta$ depends on $n$ and $h$ as

• A
  $\Delta = h \sin^2 \frac{\pi}{n}$
• B
  $\Delta = h \left( \frac{1}{\cos(\frac{\pi}{n})} - 1 \right)$
• C
  $\Delta = h \sin(\frac{2\pi}{n})$
• D
  $\Delta = h \tan^2(\frac{\pi}{2n})$