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Q.

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=hcos⁡θ−hFor regular polygon q = p / n             (n is number of sides)Δ=hcosπ/n−h=h1cosπ/n−1
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