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Find out the location of centre of mass ...

Find out the location of centre of mass of a uniform rod.

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Suppose a rod of mass M and length L is lying along the x-axis with its one end at x=0 and the other at x = L
Mass per unit length of the rod =`M/L`
Hence, mass of the element PQ of length dx situated at a distance V from the origin is dm =`M/L` dx
The coordinates of the element PQ are (x, 0,0). Therefore, x -coordinate of CM of the rod will be:
`x_(CM) = (int_(0)^(L)xdm)/(intdm) =(int_(0)^(L)(x)(M/Ldx))/M = I/L int_(0)^(L) xdx = L/2, y_(cm) =(int ydm)/(int dm)=0`
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Knowledge Check

  • Two uniform rods A and B of same diameter having length 2m and 3m and having mass per unit 4kg m^(-1) and 6kgm^(-1) respectively are joined end to end. The position of centre of mass of combined rod from the free end of A

    A
    `(71)/(26)m`
    B
    `(26)/(71)`
    C
    `(41)/(36)m`
    D
    `(36)/(41)m`

  • Two uniform rods A and B of same diameter having length 2m and 3m and having mass per unit 4kgm^(-1) and 6kgm^(-1) respectively are joined end to end. The position of centre of mass of combined rod from the free end of A

    A
    `(71)/(26)m`
    B
    `(26)/(71)m`
    C
    `(41)/(36)m`
    D
    `(36)/(41)m`

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