EXAMPLV. 



baa both cmln attached to a given weight; find the 



b-t\v n ti.- MM/H. 



10. Three eoiuil i. s, baring their baaea down- 



wards, arc placed in conta* u a horizontal 



table ; if A smooth sphere of the same substance and equal 



< be plat n- \\jll lr equilibrium 



>t, according aa the coefficient of friction between the 



res and the table is greater or leas than 



11. A uniform rod rests wholly within a rough hcmi- 



:ical bowl in a vertical plane through its centre, prove 



that the limiting position of equilibrium will be given by the 



- tin it 



" 



n of the rod to the horizon, 2/9 the 

 angle it subtends at tlie centre, and tane the coefficient of 



i rod rests in a horizontal position between two 



rough planes equally I to the horizon, and whoae 



iation to each other is 2a; if ^ be the coefficient of 



the greatest possible inclination of the line of 



: section of the planes to the horizon is tan" 1 -/- 



BUI a 



A surface is formed bjr the revolution of an equi- 

 lateral hyperbola about one of its asymptotes which i* 

 ticnl ; Hhetv that a particle will rest upon it, supposing it 

 rough, anywhere beyond t section of the surface with 



a cert 



11. A heavy particle under the action of gravity will rest 



x* t/* 

 on a rough paraboloid - + g-2, if it be placed on the 



surface at any point above the curve of intersection of the 



a? v* 



surface with the ( ^ - /** ; the axis of the para- 



boloid being vertical, its vertex upwards, and /* the coefficient 



