60 



11. A flat semicircular board with 



1 edge upwards rests on a smooth horizontal |>l:m 

 is pressed at two giv. cin-inni'cn-nr,- l,y l\v<> 



. slide in smooth vertical tubes; find the ratio 

 of tli - of the beams tliat tin- board may be in rqui- 



libriuin. 



12. Two smooth cylinders of equal radii just fit in bet\ 

 two parallel vertical walls st on a smooth horizontal 

 plan.- wit -sing against tin- walls; if a t Imler 

 be placed on the top ot them, iind the resulting pressure 

 aga: .ill. 



13. A smooth circular ring rests on two pegs not in the 

 same horizontal plane; find the pressure on each peg. 



14. Two spheres are supported by strings attached to a 



it. and rest against one another; Iind th< 

 of the strings. 



15. Two equal smooth spheres, connected by a striiu 

 laid upon the surface of a cylinder, the string being so short 

 as not to touch the cylinder; determine the position of rest 



t he tension of the string. 



10. A heavy regular polygon is attached to a smooth 



vertical wall by a string which is fa>t-in-d l<> the, middle 

 point of one of its sides; the plane of the polygon is vertical 

 and perpendicular to the wall, and one of the extremities of 

 le to which the string is attached rests against the wall; 

 shew that whatever be the length of the string when the 

 polygon is in equilibrium, the tension of the string and the 

 pressure on the wall are constant. 



17. A straight rod without weight is placed between two 

 sgs, and forces P and Q act at its extremities in parallel 



irections inclined to the rod; required the conditions under 

 which the rod will be at rest and the pressures on the pegs. 



18. Forces P, Q, It, S act along the sides of a rectangle; 

 find the direction of the resultant force. 



19. Two weights P, P are attached to the ends of two 



pass over the same smooth peg and ha\e tin -ir 

 other extremities attached to the ends of a beam AB, the 



