Question

2 ft Q2) Find the coordinates for the centroid for the plate shown. 1.ft Tat-21- -3 ft

Answer 1

Giver Plate : ny E 2 ft. Н 3 eft: →a A B eft Kft from the figure; 'C' is the ceigin (al. y) = (0,0) let ze = Distance of centroid from Y- aru's & ŷ = Distance of centroid from Hranis. then; H = H, A, + A2H2 + A343 A, TA2 TA3 0 fjs here, A, оща 2 aula Az & Az = giant Y₂A2 + Y₃ A3 W AITA2+ A3 of AHGB = 1x1=1 ft2 of BCEF = 2x3 = 6 ft CDE 1 x 3x3 Distance of centroid of AHGB from Y- anis → Hy = 2+ b = 2.5 ft. (towards lept) Distance of een tuulde of BCEF from Yaris >>#2 = 2/2=ft(towards left) 2 ana = 4.5ft H2

3 3 →y, Hz = Distance of centroid of CoE from yoqaeis >> 213 = I ft. (towards Right) Y, = Distance of contraid of AHGB from He-qaci's = 1 Ye = Distance of centraid of BCEF from 1.5 ft. - Distance of Centeroid of coE from deraser's » Y₂ = 3x13 = tft. 0.5 ft. x-aris » Y₂ = 3 from eq" ; f H Distance of centraid from y-axis = á HA, & A₂H2 + AzR3 Ait Azt AB put value from (-2.5X1) +61x6)+(1x4-5) above 1t6t 4.5 II -2.5-6+4.5 11-5 ft V १] -0.3478 PE minus sign indicate left side of y-areis. D

from ५ equc Distance of centroid from ze-ares = y € y, A, t. Y₂ Azt YzAz Ait A2 TA3 * j = (0.5 x 1) + (1-5%6) + (1x4-5) Sput the calculated It 6+ 4.5 values ft > y = = 0.5 + 9 + 4.5 11.5 = 1.2174 ft. I

Centroid of the plate is at a distance of x = 0.3478 ft. towards left of y-axis & at a distance of y = 1.2174 ft. above the x-axis as shown in figure below (point O) :-

y E P O= centroid (म, ५) = (0.3478, H 1. 2074 उ 2 PP 0 →म B. C D 211 Kaft उt. * *

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And distance of centroid from left most point (point A in figure )

=
==3-03478 = 2.6522

==3-03478 = 2.6522
3-0.3478

= 2.6522 ft. from point A.

And above x-axis = 1.2174 ft.

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