JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Rotational Mechanics

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

(A) $Δ = h sin^{2} (\frac{π}{n})$
(B) $Δ = h (\frac{1}{c o s ( \frac{π}{n} )} - 1)$ ✓ Correct
(C) $Δ = h sin (\frac{2 π}{n})$
(D) $Δ = h tan^{2} (\frac{π}{2 n})$

Answer: (B)

Solution

For a regular polygon of

n

sides, when it rolls about a vertex, the center of mass rises from height

h

\frac{h}{c o s ( π / n )}

. The maximum increase is

Δ = \frac{h}{c o s ( π / n )} - h = h (\frac{1}{c o s ( π / n )} - 1)

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Single correct option

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JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Rotational Mechanics

Solution

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