1720. Let moment of sphere radius r = MK2, r = MK3, ..shell (radii r and R) = MK3, then M‚K2+ M ̧K?=MK2, but from 1718 K2=2r, and 2 5 ; .. M,K,; = M. r2 — M. 2r, but M, M, and M 5 " 1722. Expand 1720 and find the limit when r=r,; MK2 = 22 Mr2. 1723. Mr2. 1724. If the elementary mass m be referred to the intersection of the diagonals by lines parallel to the sides, and if r be its radius of gyration; mr2 = mx2 + my3 + 2mxy cos a, and therefore MK = Σ (mx3) + Σ (my3) +2Σ (mxy) cosa, but 5' 1725. Moment about axis of parabola = M and moment about tangent at vertex == M 6a2 = M ; therefore required moment 1726. If intersections of diagonals of opposite faces be joined, these will be the three principal axes, and therefore, as regards these axes, (mxy), (mxz) and (myz) are severally zero. Also, moment of side about edge = moment of edge about edge = M ; therefore moment of cube about 3 2a2 edge (= moment of side about perpendicular edge)=; therefore moment of cube about one of the principal axes form I= A cosa + B. cos3 B+C. cosy 3 A cosa gives, moment about diagonal = 3 M aR 6 1 X M 6 1727. 1731. 1727. Since the line drawn through centre of cube parallel to diagonal of face makes angles of 45°; 45° and 90° with the principal axes, moment about that line about the three principal axes, and apply the general form substitute for x from equation to ellipse, and we get 1731. Taking elliptical section parallel to axis 2a and calling the minor axis of this section z, its mass will be represent 3xz ed by M. dy. Also moment of ellipse about an axis 4abc through its centre perpendicular to its plane will be found. +b 16 abc -b 2 a2 + b2 Hence moment of ellipsoid about (x+2) xzdy. Substituting the values of x |