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 polygon is D. Then D depends on n and h as
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a
Δ=hsin2πn
b
Δ=hsin2πn
c
Δ=htan2π2n
d
Δ=h1cosπn−1
answer is D.
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Detailed Solution
Δ=d−h=hcosθ−hFor regular polygon q = p / n (n is number of sides)Δ=hcosπ/n−h=h1cosπ/n−1