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Mass of bigger disc having radius 2R is ...

Mass of bigger disc having radius 2R is M. A disc of radius R is cut from bigger disc. Moment of intertia of disc about an axis passing through periphery and perpendicular to plane is

A

`(27MR^(2))/8`

B

`(29MR^(2))/8 `

C

3.5 MR

D

2 M`R^(2)`

Text Solution

Verified by Experts

b) Surface density of motional disc is
`sigma = (M/(pi(2R)^(2)) = M/(4piR^(2))`
Mass of cutting portion is
`m_(1) = sigma xx piR^(2) = M/4`
`I= I_(1)-I_(2)`
Where,
`I_(1)` = Moment of inertia of disc about given axis without cutting portion
`I_(2)` = Moment of inertia due to cutting portion
`I = (M(2R)^(2))/2 + M(2R)^(2) - [(m_(1)R^(2))/2 + m_(1)(2R)^(2)]`
`6MR^(2) - (9MR^(2))/8 = (39MR^(2))/8`
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