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

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` ot the nearest integer is

Text Solution

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The correct Answer is:
3
`I_0=((4m)(2R)^(2))/2-3/2mR^(2)=mR^(2)[8-3/2]=13/2mR^(2)`

`I_(P)=3/2(4m)(2R)^(2)-[(mR^(2))/2+m{(2R)^(2)+R^(2)}]`
`=24mR^(2)-11/2mR^(2)=37/2mR^(2)`
`(I_(P))/(I_(O))=(37/2)/(13/2)=37/13=3`
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Knowledge Check

  • A square lamina is as shown in figure. The moment of inertia of the frame about the three axes as shown in figure I_(1),I_(2) and I_(3) respectively. Select the correct alternative.

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