Consider regular polygons with number of sides n = 3, 4, 5 ...... 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 polygton is `Delta`. Then `Delta` depends on n and h as

Options

A. `Delta=hsin^(2)(pi/n)`
B. `Delta=htan^(2)((pi)/(2n))`
C. `Delta=h(1/(cos(pi/n))-1)`
D. `Delta=hsin((2pi)/n)`

Answer

C