EXAMPLE*. 



[AMPUBB. 



1 . A cone whose semi-vortical angle is tair 1 ^ i* enclosed 



lical surface; shew that it will rest 

 in any position. 



2. A heavy uniform rod of length a moves in A vertical 

 plan. i hinge at one A string fastened 



passes over a pully in a vertical line above the 

 attached to a weight equal to half that < 

 rod, I *ts on a curve. The hi 



tin- pully above the hinge are each e<jual 

 length of the rod, and the system i* in . .-a in all 



positions. Shew that the equation to the curve is 



ally being the origin and the prime radius being vertical. 



Two rods each of length 2a have their ends united at 



igle a, and are placed in a vertical plane on a sphere of 



radius r. Prove that the equilibrium is stable or unstable 



accvnlin:; as 



sin a is > or < - 



a 



I. A prolate spheroid rests with its smaller end on a hori- 

 zontal table. Is the equilibrium stable or unstable? 



!er resU with the centre of its base in 



the highest point of a fixed sphere, end four times the 



altitude of the cylinder is equal to * great circle of the 



sing the surface* in contact to be rough enough 



-. shew that the cylinder may be ma 

 rock through an angle of 90*, but not more, without falling 



6. A very small bar of matter is moveable about one 

 mity which is fixed halfway between two centres of 

 force attracting inversely as the square of the di*tam 

 / be the length of the bar, and ia the distance between the 



