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The position vectors of three particles ...

The position vectors of three particles of mass `m_(1)= 1kg, m_(2)=2 kg` and `m_(3)=4 kg` are `vec(r )_(1)=(hat(i)+4hat(j)+hat(k))m, " " vec(r )_(2)=(hat(i)+hat(j)+hat(k))m`, and `vec(r )_(3)=(2hat(i)-hat(j)-2hat(k))m` respectively. Find the position vector of their centre of mass.

Text Solution

Verified by Experts

The position vector of centre of mass of the three particles is given by
`vec(r )_(c )=(m_(1)vec(r )_(1)+m_(2)vec(r )_(2)+m_(3) vec(r )_(3))/(m_(1)+m_(2)+m_(3))`
`vec(r )_(c )=(1(hat(i)+4hat(j)+hat(k))+2(hat(i)+hat(j)+hat(k))+4(2hat(i)-hat(j)-2hat(k)))/(1+2+4)`
` = ((11hat(i)+2hat(j)-5hat(k)))/(7)=(1)/(7)(11hat(i)+2hat(j)-5hat(k))m`
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The position vectors of three particles of mass m_(1)=1kg, m_(2)=2kg and m_(3)=4 are vec(r_(1))=(hat(i)+4hat(j)+hat(k))m, vec(r_(2))=(hat(i)+hat(j)+hat(k))m, and vec(r_(3))=(2hat(i)-hat(j)+2hat(k))m, respectively. Find the position vector of their centre of mass.

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Knowledge Check

  • If vec(F)= hat(i) + 2hat(j) + hat(k) and vec(V)= 4hat(i)- hat(j) + 7hat(k) find vec(F).vec(V)

    A
    6W
    B
    9W
    C
    13W
    D
    12W

  • If vec(F) = hat(i) + 2hat(j) + hat(k) and vec(V) = 4hat(i) - hat(j) + 7hat(k) find vec(F).vec(V)

    A
    6W
    B
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    C
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  • The angle between vec(A) = hat(i) = 2hat(j) - hat(k) and vec(B) = - hat(i) + hat(j) - 2hat(k) is

    A
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    B
    `45^(@)`
    C
    `60^(@)`
    D
    `90^(@)`

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