EX A 



OWH Weight. If II" be the weight of tin- <iiv un- 



stretched length, I its stretched length, shew that 





20. A circular elastic string is placed on a smooth sphere 

 so that tlic whole string is in one horizontal pla: 

 subtends -when nnstretched an angle L>^ at tin- 

 angle 20 when in a position of equilibrium ; shr\v that 



sin 6 = sin a 1 1 + - sin a tan 0) , 



where a = radius of sphere, and c depends on the nature of 

 the string. 



21. A heavy uniform elastic string rests horizontally on a 

 portion of a surface of revolution, of which the axis is vertical, 

 in every position : prove that the generating curve is a para- 

 bola a diameter of which is the axis of revolution. 



22. A heavy elastic string surrounds a smooth hi.ri/nntal 

 cylinder, so that the surface of the cylinder is subject to n> 

 pressure at the lowest point; find the \ ,-my point 

 of the cylinder, and the tension of the string; its modulus 

 of elasticity being equal to the weight of a portion of string 

 the natural length of which is $ of the diameter of the cylinder. 



23. A uniform heavy elastic string, whose natural Ir- 



is a, is stretched and placed in equilibrium on a rii'_ r h in- 

 clined plane; find the tension at any point, and shew that 

 the direction of the friction changes at a point of the string, 

 the natural distance of which from the upper end is 



where a is the inclination of the plane to the horizon. 



24. A heavy elastic cord is passed through a number 

 of fixed smooth rings. Shew that in the position of equi- 



