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Two bodies of masses 1kg and 3kg are lyi...

Two bodies of masses `1kg` and `3kg` are lying in `xy` plane at `(0,0)` and `(2,-1)` respectively. What are the coordinates of the centre of mass ?
Hint. `x_(cm)=(m_(1)x_(1)+m_(2)x_(2))/(m_(1)+x_(2))`, `y_(cm)=(m_(1)y_(1)+m_(2)y_(2))/(m_(1)+m_(2))`

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Verified by Experts

`x_(cm)=(1xx0+3xx2)/(4)=(6)/(4)=(3)/(2)`
`y_(cm)=(1xx0+3xx(-1))/(4)=-(3)/(4)`
`(x_(cm),y_(cm))=((3)/(2),-(3)/(4))`
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Knowledge Check

  • Two bodies of mass 2 kg and 5 kg have position (1 m, 2 m, 1 m) and (3 m, 2 m, -1 m) respectively. The position vector of centre of mass is

    A
    `(frac{17}{7}hati + 2hatj - frac{3}{7}hatk)m`
    B
    `(17hati + 14hatj - 3hatk)m`
    C
    `(2hati + frac{17}{7}hatj - frac{3}{7}hatk)m`
    D
    `(14hati + 17hatj - 3hatk)m`

  • 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`
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