. A text book of elementary mechanics, for the use of colleges and schools. w Fig. 104. 2 fore —77 hut gg = fs, hence gG = $$, and 180 STATICS. [171. the centre of gravity of W be at G, of w9 at g9, and ofthe remainder (w) at g99. Join g9 and G, and take on the line produced ~4~f — ~r, — tff ,1 then is a the r Gg9 to W—tv9 u required point. For example, let the whole body be a circle ABC(Fig. 105) whose centre is G; and the part a second. Fig. 105. circle whose centre is g9, and whose diameter is the w9 1radius (R) of the larger circle. Then — = —, and W or ZT*) =: q 5 also> 9fG — ^R\ hence
. A text book of elementary mechanics, for the use of colleges and schools. w Fig. 104. 2 fore —77 hut gg = fs, hence gG = $$, and 180 STATICS. [171. the centre of gravity of W be at G, of w9 at g9, and ofthe remainder (w) at g99. Join g9 and G, and take on the line produced ~4~f — ~r, — tff ,1 then is a the r Gg9 to W—tv9 u required point. For example, let the whole body be a circle ABC(Fig. 105) whose centre is G; and the part a second. Fig. 105. circle whose centre is g9, and whose diameter is the w9 1radius (R) of the larger circle. Then — = —, and W or ZT*) =: q 5 also> 9fG — ^R\ hence -7TJT = q > JF - w \ wl 3 » £ > Gg9 3; and Gg99 = -J-JK. EXAMPLES. XXIV. Cto-6 e?/ ^ra«%. Articles 159-171. [The connecting rods mentioned are supposed to be rigid, and,except when otherwise stated, to be uniform and withoutweight. ] 1. Where is the centre of gravity of two bodies, A and B,weighing 4 and 5 lbs. respectively, rigidly connected by a weightless rod 24 inches long? 2. Three weights of 3, 6, and 12 lbs. are hung, at A, B, and G 171.] CENTRE OF GRAVITY. 181 respectively, on a rigid bar; AB = 6 inches and BC — 12 inches:Where will the bar balance? 3. Four weights of 2, 3, 5, and 6 lbs., at A, B, C, and D, areconnected rigidly in a straight line; AB = 10, BC = 8, CD = is their centre of gravity? 4. A rod AB, 18 inches long and weighing 4 ounces, has aweight P— 2 lbs. hung at the end B: Where w
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