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The problem I am attempting is the following enter image description here

I got pretty far into it, however, I was not able to do the last step of the solution. The given solution is here

enter image description here

What I don't understand: I don't understand where the last equation comes from. Can someone clarify where it comes from?

Maths Wizzard
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    do you know about equilibrating moments ? – G Cab Nov 14 '20 at 14:47
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    In the diagram, we are taking moments about an axis through the point of contact with the table, and perpendicular to the plane of the page. The left-hand side of the equation gives the clockwise component due to gravity, and the right-hand side gives the anticlockwise component due to the tension in the string. – TonyK Nov 14 '20 at 14:48
  • @GCab no I have not. Is this what the answer is using? If yes do you know of any good resources through which I can learn about it? – Maths Wizzard Nov 14 '20 at 14:48
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    yes, the answer is using that principle, and, well, that is a fundamental chapter of any course in Statics – G Cab Nov 14 '20 at 14:51

1 Answers1

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It's just the moment of force balance. In the statement of the problem, it's said that the distance from the axis to the center of mass is $\cfrac{3\pi a\sin \theta}{16\theta}$.

Basically, in the following formula $$F_1 l_1 = F_2 l_2$$ we have $F_1 = \cfrac{Mg\theta}{\pi}$,$~ l_1 =\cfrac{3\pi a\sin \theta}{16\theta}$ and $F_2 = 2T\sin \theta$, $~l_2 = a$.

VIVID
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