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

Answer

D

Explanation

`cos ((pi)/(n)) = h/R`
`Delta = R - h = (h)/(cos (pi/h)) - h = h [(1)/(cos (pi/n) - 1)]`