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A lamina is made by removing a small dis...


A lamina is made by removing a small disc of diameter 2 R from a bigger disc of uniform mass density and radius 2R, as shown in figure. A second similar disc is made but instead of hole a disc of triple the density as of first it filled in the hole. Centre of mass is calculated in both the cases and was found at a distance `r_(1) & r_(2)` from centre `O` respectively find the ratio `|(2r_(2))/(r_(1))|`

Text Solution

Verified by Experts

The correct Answer is:
2
`r_(1)=([-sigmaxxpiR^(2)]xxR)/([-sigmaxxpiR^(2)]+[sigmaxxpi(2R)^(2)])`
`&r_(2)=([2sigmaxxpiR^(2)]xxR)/([2sigmaxxpiR^(2)]+[sigmaxxpi(2R)^(2)])implies|(2r_(2))/(r_(1))|=2`
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Knowledge Check

  • A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing though O and P is I_O and I_P respectively. Both these axes are perpendicular to the plane of the lamina. The ratio I_P/I_O is

    A
    `13//37`
    B
    `37//13`
    C
    `73//31`
    D
    `8//13`

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