178 ANSWERS. 



,aa+ 26' (2a b + ' 



=4-5 



o.33 a > 0.25 <r. 

 (*5) * = - 



(26) For a segment of a ring of angle 2 a and radii r 1? r 2 , the dis- 



tance of the centroid from the centre is x = f . ^-^A^_ 2 . 



a n + >2 



Hence ^ = ^ (740 + 73 Vi) = 3.22 ft. ; i.e. the centroid lies about 



I477T 



8^ in. above the door. 



(27) * = $*, J = f> 



(28) ^ = , J = - 



(32) Take the vertex as origin, the axis of the cone as axis of x r 

 and one of the bounding planes as plane of xy. Then, if a be the 

 radius of the base, h the height, and 2 a the angle at the vertex of the 

 cone, the formulae of Art. 40 give 



, - 7 - 9 sn d> - o i cos 



hence * = A, .? = -Z, s = --- - 



(33) About 2631 miles from the centre. 



(34) Regard the ice-cap as a surface mass of density 8 ; let Xi be the 

 distance of its centroid from the earth's centre, m l the mass of the ice- 

 cap, m that of the earth alone, and <f>' the polar distance of the arctic 

 circle ; then the equation of moments (m + m l )x= m^i gives, if m\ in 

 the parenthesis be neglected, x = (m l /m)x l =^ sin 2 <' = 0.216 mile. 



(35) At the distance \r from the centre. 



(36) x = 



