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Consider regular polygons with number of sides n = 3, 4, 5 ...... as shown in the figure. The centre 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 centre of mass for each polygon is Δ . Then Δ depends on n and h as h h h

1. Δ = h ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 1 n cos 1
2. Δ = h tan 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π n 2
3. Δ = h sin ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π n 2
4. Δ = h sin 2 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π n

Correct answer: Δ = h ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π 1 n cos 1

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