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