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Three particles of masses m(1)=1kg, m(2)...

Three particles of masses `m_(1)=1kg, m_(2)=2kg` and `m_(3)=3kg` are kept at the vertices of an equilateral triangle of side 1 m. What is the x co-ordinate of its centre of mass?

A

`3/4m`

B

`4/5m`

C

`6/7m`

D

`7/12m`

Text Solution

Verified by Experts

The correct Answer is:
D

In this case, for `m_(1), (x_(1),y_(1))=(0,0)`
For `m_(2),(x_(2),y_(2))=(1,0)`
For `m_(3),(x_(3),y_(3))=((1)/(2),(sqrt(3))/(2))`
`therefore` The x co-ordinate of the centre of mass is given by
`X_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`=(1xx0+2xx1+3xx(1)/(2))/(1+2+3)=(7)/(12)m`
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