Question

Question 2: For the shaded area shown in the figure a. Find the coordinates of the centroid. b. Calculate the moment of inertia about y-axis. Y to h/2 1m * -- h” h/2 2m Hole * X X 1m 2m 3m 2m 1m 3m 2h/3 t X bh 36 h/3 + X

Answer 1

Solution in Criven that in ay & Reference asis scentroidal -y-axis 5.177m K lim Centroidal gaasis 2m Refrena no fim من مه 2 m 3m am X im 3m Co-ordinate of Centroidi (Ax, St Anda) -(A₂73) + Aux Aid Aza Azt Ay A, & * 2*4 = you?, x= 2*2= 2 = 1.333m Aga 6x4=24m2, Xa=5m Az= 2*2= ym², x3=6m Ay = 1/2*3*4 = 6m2, nuagm

Substitute all value, we get. (4*6) & (649) * = [4*1.333) + (2446) - ५। 24 - ५ +6 x=5.197m Auf G= % = Aiga Astz - Azyat Augu Antha-Azt Ay § m,= 1.333m • ₂=am, Yg=en Yo = ma1333m Substitute all value we get g 14 1:333) & (24429 = 22 + (641333) Mot ruu ts = 1.777m And

b) Moment of Inertial about yo asis) in х А? «Ssa хблач Iyya I nyt fyy, & fyy Туу - Тух, + S4, — Sчя, - Туу (1) nero » Tчч с сеъ & A, hi - Чж (чя 3-ga-) З 59.963m >44, 3 сач- & Azhar Ч+ 3 + (24xo-1-) ч - 2 75m - (чя. 1.2-) = (19: 625 vЧ - ху 2 - Tчач с Ч% З ЗС Com eдмін + 16 3231) - [90 -691 Тух = 59 - 963 + 2:5 — 14.424, +9ь •691 Тgy = 2bg - M bg