Question

5. Calculate the y coordinate of the centroid the hatched area shown. 10 cm 10 cm 16 cm 6 cm 6 20 cm

Answer 1

(20, 10 Jem locny na?ny i x 20cm 710 1/41 Jo we first Calculate area and Centroid of curve part consider a small strip of length (n) and width dy at a distance ofy Rom a -cixis. Area of small sirip dA = rody da = xody 3 r2- yoy 2. trový Jan = /veorg-dy A = Vuos vs. dy A = Vuo [* A = Vuo [ A = 250 [ 10% ] A = 2V40 x 1042 = 90 com and let it's its centroid weaked at 7. Jo A a fonda a lvoready = fyrio vy.dy GoA = V70 1742.49 3.n e vão J.A - V40 I 742710 = 2V70 x 10542 J an = Eco - 80 = 6cm 40% I 5/ 2u YA

Given fig. is o Areraj) dhe 10cm Lim zoom 6cm - 6cm The given Area (A1) o 6cm aree divided into 4 area- Panabola Area A1 = go cm2 o y a 6om { distance of a 4 from a axis © Rectangle Area (42) = 10x12 = 120cm2 yz = Distance of Cz from n-aris = 10/2= sem ② Triangle t h = to em Area Az = {xbxh = x 12410 = 60 cm2 - Iz = Distance of Cg from ar-axis = p Au = A xd = 2 x 62 a on cm2 Ea yy = d/= 6/2 = 3cm. tince

I = opstance of centroid from n-axis У – А, Эt A271-t A53, — эч A+Azt Az - Ay Au is minus because it has to removed J = 400*6 + 120x57 60x64) - 98 (3) no +120 +6o-oh 15= 3-91209 cm | Amor y coordinate of hatched area