BOOK OF MATHEMATICAL PROBLEMS. 



jectcd at right angles to the string; prove that the greatest angle 

 which the string can make with the rod produced is 



where m, p are the masses of the rod and particle. 



Prove that if, after any time t> the rod and string make 

 angles 0, <j> with their initial positions, 



where &* = a 9 -*-= - , and v is the initial velocity of the particle. 



1534. A circular disc capable of motion about a vertical axis 

 through its centre, normal to its plane, is set in motion with 

 angular velocity fi, and at a given point is placed freely a rough 

 uniform sphere : prove the equations of motion 



dO 



r, 6 being the polar co-ordinates of the point of contact measured 

 from the centre of the disc, o> the angular velocity of the disc, 



I the initial value of r, and #* = , where m, p are the masses of 

 the sphere and disc, and c the radius of the disc. 



1535. A circular disc lies flat on a smooth horizontal table 

 on which it can move freely, and has wound round it a fine string 

 carrying a particle, which is projected with a velocity v 'from a 

 point of the disc in a direction normal to the disc: prove that 



