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Two thin discs each of mass M and radius...

Two thin discs each of mass `M` and radius `r` are attached as shown in figure, to from a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc `B` and passing through its centre is :
.

A

`2Mr^(2)`

B

`3Mr^(2)`

C

`4Mr^(2)`

D

`5Mr^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Moment of inertia of discs `A` and `B` about the axis through their cenre of mass and perpendicular to the plane will be
`I_("AA")=I_(BB)=1/2Mr^(2)`
Now moment of inertia of disc `S` about an axis through `B` by theorem of parallel axis will be
`I_("AA")=I_(BB) +M(2r)^(2)=1/2Mr^(2)+4Mr^(2)=9/2Mr^(2)`
So, `I=I_(BB)+I_(AB)=1/2 Mr^(2)+9/2Mr^(2)=5Mr^(2)`
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Knowledge Check

  • Two thin discs each of mass M and radius r metre are attached to form a rigid body as shown in figure. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is

    A
    `2Mr^2`
    B
    `3Mr^2`
    C
    `4Mr^2`
    D
    `5Mr^2`

  • M.I. of a thin uniform circular disc about one of the diameters is I. Its M.I. about an axis perpendicular to the plane of disc and passing through its centre is

    A
    `sqrt2 I`
    B
    2I
    C
    I/2
    D
    I/4

  • From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

    A
    `4 MR^(2)`
    B
    `40/9 MR^(2)`
    C
    `40 MR^(2)`
    D
    `37/9 MR^(2)`

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