three particles of masses 1kg, 2kg, &3kg respectively are placed atcorners of an equilateral tringle of side 10cm . find cordinates of centre of mass.
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Answer:
Assume , Point A is origin.
From the figure, CP=1×sin(60
o
)=
2
3
Centre of mass from Point A in direction of x−axis, x
cm
=
m
A
+m
B
+m
C
m
A
x
A
+m
B
x
B
+m
C
x
C
⇒x
cm
=
1+2+3
1×0+2×1+3×
2
1
=
12
7
Centre of mass from Point A in direction of y−axis, y
cm
=
m
A
+m
B
+m
C
m
A
y
A
+m
B
y
B
+m
C
y
C
⇒y
cm
=
1+2+3
1×0+2×0+3×
2
3
=
4
3
So coordinate of centre of mass (
12
7
,
4
3
), Distance from A, =
(
12
7
)
2
+(
4
3
)
2
=
6
19
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