Consider regular polygons with number of sides $n = 3,4, 5 \dots$ 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 $Δ$ . Then, $Δ$ depends on $n$ and $h$ as

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Aicharya · Accepted Answer

O A = h O B = h cos ⁡ π n Initial height of C O M = h Final height of C O M = h cos ⁡ π n ∴ Δ = h cos ⁡ π n - h Δ = h 1 cos ⁡ π n - 1

Consider regular polygons with number of sides n = 3,4 , 5 … as shown in the figure. The center of mass of…

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