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Three rods of the same mass are placed a...

Three rods of the same mass are placed as shown in the figure. Calculate the coordinates of the centre of mass of the system.

Text Solution

Verified by Experts

The correct Answer is:
`((a)/(3),(a)/(3))`
`x_(cm) = ((M xx (a)/(2)) + (M xx 0) + (M xx (a)/(2)))/(M + M + M) = (a)/(3)`
`y_(cm) = ((M xx 0) + (M xx (a)/(2)) + (M xx (a)/(2)))/(M + M + M) = (a)/(3)`
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Knowledge Check

  • Three rods of the same mass are placed as shown in the figure. What will be the co-ordinates of the cneter of mass of the system ?

    A
    `( a//2, a//2)`
    B
    `( a//sqrt( 2), a//sqrt(2))`
    C
    `((sqrt(2)a)/(3), ( sqrt( 2)a)/(3))`
    D
    `((a)/(3), ( a)/( 3))`

  • A wire of uniform cross-section is bend in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The co-ordinates of the centre of mass of the system are. .

    A
    `((15 l)/(14), (6l)/(7))`
    B
    `((15 l)/(14),l)`
    C
    `(l, (l)/(2))`
    D
    `(l, l)`

  • A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure. The y- coordinate of the centre of mass of the system is

    A
    `(2r)/(pi)`
    B
    `-(6r)/(3pi+2)`
    C
    `-(2r)/(pi)`
    D
    Zero

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