200 LANEOUS EX A Mr: 



28. A ball of p' rht and radius 5^ hung by a || 



of given length fn.m which is also atfc 



by a string so lung tliat tin- 

 hangs below the ball; find tin- angle which the Mr! 

 which the ball is atta kefl with the vertical. 



Result. Let Q be the weight of the ball, /' the weight 

 which hangs below the l.all. a tin- radius of the ball, / the 

 length of the string: then the inclinaii ,\\ <,f the string \ 



vertical is sin" 



29. A right cone whose axis is a and vertical angle is 

 2 sin' 1 * /( =) is placed with its base in contact with 



vertical wall, and its curved surface on a smooth li<>ri/.<>ntal 



rod parallel to the wall ; .shew that it will remain at ; 



the distance of the rod from the wall be not greater than a 



nor less than _ 



30. A paraboloid is placed with its vertex downward 

 axis vertical between two planes each inclined to the horizon 

 at an angle of 45; find the greatest ratio which the height of 

 the paraboloid may have to its latus rectum, so that, if it Le 

 divided l>y * plane through it- 1 th- lino of intersec- 



tion of the inclined plane-, the two parts may remain in 

 equilibrium : also find the least ratio. 



Result. Let h be the height and 4a the latus rectum ; then 

 the greatest and least ratios are determined respectively l>y 



'11. Three bars of given length are maintained in a hori- 

 zontal position, and tied together at their xtn inities so as 

 to form a horizontal triangle; and a smooth sphere of 

 weight and size rests upon them. Find the pressure of the 

 sphere on each bar. 



