ANSWERS. 235 



(13) (a) 



(14) I= 



Pages 137, 138. 



The square of the radius of inertia is : 



(2) 

 (3) 



(4) f * 2 . . 



(5) i(^i 2 + ^2 2 ) ; in the limit, /= Ma 2 . 



(6) Differentiating the moment of inertia in Ex. (4), we find 

 J= M.\a\ 



(7) (*H* 2 ; m* 2 ; Wi** + K- 



(9) (*)K; (6)<*i (c)^(a 2 + b 2 ). 



(10) 



(12) For axis parallel to b, /= J8[t(A 3 + ^) +^(^ + 8) 2 ] ; for axis 

 parallel to h, I f 8(1 /^ 3 4- ^S 2 ) ; for perpendicular axis, 

 /= 8[/^ 3 + ^ + 3 bh* 



Pages 149, 150. 



(i) The centroidal principal axes are perpendicular to the faces. 

 The moments for these axes are J- M(& 2 +c 9 -), 1 M(c 2 +a 2 ), | M(a?+P). 

 The central ellipsoid is ( 2 + ^ 2 )^+ (^ + a 2 )/ 4- ( 2 + <*V= 3 e 4 . 

 For an edge 2 a, f=$M(P+<*) ; for a diagonal I= 



For the cube the central ellipsoid becomes a sphere of radius 

 for an edge of the cube, /= ^- a 5 . 



(2) Central ellipsoid : (P + r>) ** + (^ 2 + 2 ) / + (<* + ^ 2 ) ^ 2 = 5 e 4 ; 

 for/,^ = i(6a 2 + ^ 2 ). 



(3) Take the vertex as origin, the axis of the cone as axis of x\ 

 then /j = -f^Ma 2 ; //, i.e. the moment of inertia for the jy-plane,=| Mh 2 . 

 As for a solid of revolution about the axis of x B* = C 1 and ^ = (7, we 



