four particles of mass 1kg 2kg, 3kg and 4 kg are placed at the four vertices A,B,C,D of square of side 1m find the position of centre of mass of the particles
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Answer:
Assuming D as the origin. DC as x-axis and DA as y-axis we have
m
1
=1kg,(x
1
,y
1
)=(0,1m)
m
2
=2kg,(x
2
,y
2
)=(1m,1m)
m
3
=3kg,(x
3
,y
3
)=(1m,0)
m
4
=4kg,(x
4
,y
4
)=(0,0)
Coordination of their CM are calculated as follows.
x
CM
=
m
1
+m
2
+m
3
+m
4
m
1
x
1
+m
2
x
2
+m
3
x
3
+m
4
x
4
=
1+2+3+4
(1)(0)+2(1)+3(1)+4(0)
10
5
=
2
1
m=0.5m
Similarly, y
CM
=
m
1
+m
2
+m
3
+m
4
m
1
y
1
+m
2
y
2
+m
3
y
3
+m
4
y
4
=
1+2+3+4
(1)(1)+2(1)+3(0)+4(0)
=
10
3
m=0.3m
∴(x
CM
,yCM)=(0.5m,0.3m)
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