KX AMPLE*. I.".'' 



II. A r. w chain in fastened at its cxtrcn 



on smooth rod* 



vl plane ncd at the time angle 



al; find the condition thnt the tension at the 



lowest I'.'int nmy be < weight of the chain; 



.tie shew that the v< tance of the rings 



cction of the rods is 



1 cot a log (I + V2), 



I IB the length of the ch 



The density at any point of a catenary of variable 

 ty varies as the radios ot curvature ; determine the equa- 

 te catenary. 

 Rttult. The curve : '.0. 



A heavy c-rl with one end fixed to a point in the 



of a smooth horizontal passed bclov. 



arricd round over the toj :*ing 



allowed to hang freely. Shew that unless the portion v, 

 hangs vertically be longer diameter of the cylinder, 



the * flf, so as to hang down from the fixed point 



issing below der. 



a uniform string hang in th<> form of a parabola 

 by the ac-ti n of normal forces only, the force at any point P 

 varies as (8P)~* t S being the focus. 



without weight touch a given cylinder in 



jth part of its circumference and in a plane perpendicular to 



its axis, what tension at one extremity will support a weight 



H)lbs. suspended at the other, frit: - supposed to 



be ^th part of the pressure? To what will this tension be 



teed if the string is wound round 1 tli circumferences? 



/A = i, And a string without weight pastes twice 



1 a post, y taking approximate values of e and IT, 



1 support another more than twenty times 



as :;ivat. 



scales, one containing a weight P and the 

 other a weight Q, be suspended by a string without weight 



