find-the-center-of-gravity-with-respect-to-point-O-

Question Number 151096 by john_santu last updated on 18/Aug/21

find the center of gravity with respect to point O

Commented by john_santu last updated on 18/Aug/21

Commented by Olaf_Thorendsen last updated on 18/Aug/21

∙ A big full square :

S_{1} = 10 \times 10 = 100 {cm}^{2}

Ω_{1} (5, 5)

∙ A small empty rectangle :

S_{2} = - 4 \times 2 = - 8 {cm}^{2}

Ω_{2} (8, 3)

∙ A small empty rectangle :

S_{3} = - 4 \times 2 = - 8 {cm}^{2}

Ω_{3} (8, 7)

S = S_{1} + S_{2} + S_{3} = 100 - 8 - 8 = 84 {cm}^{2}

S \vec{OG} = S_{1} \vec{O Ω_{1}} + S_{2} \vec{O Ω_{2}} + S_{3} \vec{O Ω_{3}}

\vec{OG} = \frac{100}{84} (5, 5) - \frac{8}{84} (8, 3) - \frac{8}{84} (8, 7)

G (\frac{31}{7}, 5)

Commented by john_santu last updated on 18/Aug/21

how to get Ω_{1} (5, 5) .

Commented by Olaf_Thorendsen last updated on 18/Aug/21

the square is 10 \times 10 .

the center of gravity is (5, 5) .