308 BOOK OF MATHEMATICAL PROBLEMS. 



a horizontal axis through one extremity, through 90 to their 

 lowest positions, and the pressures on the axes in those positions 

 are equal; prove that their weights are as 35 : 34. 



147G. The centre of percussion of a triangular lamina, one of 

 whose sides is a fixed axis, bisects the straight line joining the 

 opposite angle with the middle point of the side. 



1477. A lamina ABCD is moveable about AE which is 

 parallel to CD; prove that its centre of percussion will be at the 

 intersection of AC, BD, if AB a 



1178. In the motion of a rigid body about a horizontal axis 

 under the action of gravity, prove that the pressure of the axis 

 can only be reduced to a single force, throughout the motion, 

 when the axis of revolution is a principal axis at the point M 

 which is nearest to the centre of gravity. If the axis be a princi- 

 pal axis, but at another point N, and the pressures on the axis be 

 reduced to two, at M and N respectively, the former will be equal 

 and opposite to the weight of the body. 



1479. A rough uniform rod, length 2a, is placed with a 

 length c(> a) projecting over the edge of a horizontal table, the rod 

 being perpendicular to the edge; prove that the rod will begin to 

 slide over the edge when it has turned through an angle 



tan 



2 +9(c-a) 2 * 



1480. A uniform beam capable of motion about one extre- 

 mity is in equilibrium ; find at what point a blow must be applied, 

 perpendicular to the rod, in order that the impulse on the fixed 

 extremity may be equal to one-eighth of the blow. 



1481. A uniform beam, moveable about its middle point, is 

 in equilibrium in a horizontal position ; a perfectly elastic particle 

 whose mass is one fourth that of the beam is dropt upon one 

 extremity, and is afterwards grazed by the other extremity; prove 

 that the height from which the particle falls is to the length of 

 the beam :: 49 (2/i + !)TT : 48, n being integral. 



