Find the centre of mass of three particles at the
vertices of an equilateral triangle. The masses of the
particles are 100 g, 150 g and 200 g respectively.
Each side of the equilateral triangle is 0.5 m long.
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Let
m
1
=100g,m
2
=150g,m
3
=200g
a=0.5m=50cm
Center of mass coordinates:-
x=
m
1
+m
2
+m
3
[
2
−a
×m
1
+0×m
2
+
2
a
×m
3
]
=
2(m
1
+m
2
+m
3
)
(m
3
−m
1
)a
=
2×450
(200−100)50
=
9
50
cm
y=
m
1
+m
2
+m
3
(0×m
1
+
2
3
×a×m
2
+0×m
3
)
=
m
1
+m
2
+m
3
2
3
×a×m
2
=
450
2
3
×50×150
=
3
25
cm
y coordinates of the centroid of the triangle
=
3
1
×
2
3
×a=
3
25
cm
∴ the center mass is
9
50
cm.
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