BOOK OF MATHEMATICAL PROBLEMS. 



librium inclined at an angle a to the vertical, one of the strings is 

 cut; prove that the initial tension of the other string is 



m + 3p sin* a' 

 and that the radius of curvature of the initial path of the particle 



j s M 1' a m. p being the masses of the rod and of either 

 m COB a ' 



particle, and I the length of the string. 



1487. A uniform rod, moveable about one extremity, is held 

 in a horizontal position, and to a point of the rod is attached a 

 heavy particle by means of a string ; prove that the initial tension 

 of the string when the rod is let go is 

 nipga (4a 3c) 



m, p being the masses of the rod and particle, 2a the length of the 

 rod, and c the distance of the string from the fixed extremity. 



Prove that the initial path of the particle is the curve whose 

 equation, referred to horizontal and vertical axes, is 

 ma (4a - 3c) if + $Qc 2 l(rna + pc) x = j 

 / In ing the length of the string. 



1488. A uniform rod, moveable about one extremity, has 

 attached to the other extremity a heavy particle by means of a 

 string, the rod and string are initially in one horizontal straight 

 line and without motion; prove that the radius of curvature of 



the initial path of the particle is - j-, a f b being the lengths of 



tt 4- /0 



the rod and string. 



1489. A uniform rod, of length 2a and mass m, capable of 

 motion about one extremity, is held in a horizontal position, and 

 on it slides a small smooth ring of mass p : if the rod be let go, 

 the radius of curvature of the path of the ring is initially 



P \ 

 m a) ' 



4 - 3 

 c being the initial distance of the ring from the fixed extremity. 



