JEE Advanced 2017 · Paper 2 · Physics Q2

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PhysicsSingle correct+3 / -1Question 2 of 54

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

A triangle, a square and a pentagon standing on a horizontal line, each with its centre of mass at height h; for each, a dashed copy shows the polygon tipped over its leading (right) vertex as it rolls, with a curved arrow indicating the rotation.

\Delta = h\sin^2\left(\frac{\pi}{n}\right)

\Delta = h\left(\frac{1}{\cos\left(\frac{\pi}{n}\right)} - 1\right)

\Delta = h\sin\left(\frac{2\pi}{n}\right)

\Delta = h\tan^2\left(\frac{\pi}{2n}\right)

Answer and worked solution

Official answer: B

Heights. The centre of mass is at the polygon's centre, at height $h$ (the inradius) when a side rests on the ground. As the polygon tips over its leading vertex, the centre is highest when it is directly above that vertex. Its height is then the circumradius:
$R=\frac h{\cos(\pi/n)}.$

Rise.
$\Delta=h\left(\frac1{\cos(\pi/n)}-1\right).$

(B)

Topics:Rolling motion Centre of mass

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JEE Advanced 2017 · Paper 2, Physics question 2