Question

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 center of mass for each polygon is A. Then A depends on n and h as?
(JEE (Advanced) 2017;P-2, 3/61,-1]​

Answer 1

Answer:

The answer will be option D

Explanation:

According to the problem the height of the position of the polygons from the ground is h.

Now we know that for any n sided polygons

h/x = cos (π/n) => x = h/cos(π/n)

Again we also know that,

Δ = x-h

by substituting the value of x,

Δ =  h/cos(π/n) -h

Δ = h( 1/cos(π/n) -1)

Therefore A depends on n and h as h( 1/cos(π/n) -1)