Centre of Mass 1 Question 6
6. Consider regular polygons with number of sides $n=3,4,5 \ldots \ldots$ 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 each polygon is $\Delta$. Then, $\Delta$ depends on $n$ and $h$ as
(2017 Adv.)
(a) $\Delta=h \sin ^{2} \frac{\pi}{n}$
(b) $\Delta=h \sin \frac{2 \pi}{n}$
(c) $\Delta=h \tan ^{2} \frac{\pi}{2 n}$
(d) $\Delta=h \frac{1}{\cos \frac{\pi}{n}}-1$
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Answer:
Correct Answer: 6. (d)
Solution:
$$ \cos \frac{\pi}{n}=\frac{h}{R} $$
