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Three masses 2kg, 4kg and 6kg are placed...

Three masses 2kg, 4kg and 6kg are placed in the XY plane with respective coordinates (0,0),(0,2) and (2,2). The coordinate of their centre of mass is

A

(1,2)

B

(1,1.67)

C

(2,1.67)

D

(1.67,3)

Text Solution

Verified by Experts

The correct Answer is:
B
`X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`=(2xx0+4xx0+6xx2)/(2+4+6)=12/12=1`
`Y_(CM)=(m_(y)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))`
`=(2xx0+4xx2+6xx2)/(2+4+6)=(8+12)/12`
`=20/12=5/3=1.666=1.67`
`:.` Centre of mass is `(X_(CM),Y_(CM))=(1,1.67)`
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