A frame made of thin wire of line density 'p'has the shape of a circle of radius 'a' together with a diameter AB of the

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A Frame Made Of Thin Wire Of Line Density P Has The Shape Of A Circle Of Radius A Together With A Diameter Ab Of The 1 (110.54 KiB) Viewed 15 times

A frame made of thin wire of line density 'p'has the shape of a circle of radius 'a' together with a diameter AB of the circle. The frame lies on a smooth horizontal table and is free to rotate about a fixed vertical axis through a point 'O' on the circumference of the circle and on the diameter 1 normal to AB. An insect of mass -as initially at 3 as initially at rest at ‘A’ begins to crawl along the diameter AB. If ¢ is the angle turned backwards by the frame in space after the insect has crawled a distance x along AB, show that : 2 575 {n?a? +(a= x - = في {2( 0 = = ax . = where · is differentiation w.r.t. t and n2 1211 + 9. Prove also that when the insect reaches B, the frame will have rotated through an angle : 7 2n - tan n 2 n' -1