# N-Pod.

Consider an n - pod consisting of $$n$$ uniform bars (legs) of length $$a$$ and mass $$m = 0.8 kg$$ , freely jointed at point A. The middle points of the legs of the n-pod are joined by $$n$$ massless strings of length $$b$$ . The n-pod rests on a smooth surface while supporting a camera of mass $$M = 1 Kg$$ . For $$n=3$$, figure is:

For $$\frac{a}{b} = \eta$$, find an expression for tension in the strings. Considering this expression for $$\eta = 4$$, let the maximum value of $$n$$ for which tension $$T$$ in the strings is real be $$N$$, and the tension in the strings for $$n=N$$ be $$T$$ (in newtons) , find $$T \times N$$ rounded to the nearest integer.

Details and assumptions:-

• $$g = 9.8 m/s^2$$

• The arrangement is symmetric , i.e. the points where legs meet floor form a regular n-gon

• This problem has been inspired by a past brilliant problem Tripod

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