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Two rings of same radius and mass are pl...

Two rings of same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass the ring `= m`, radius `= r`)

A

`1/2 mr^2`

B

`mr^2`

C

`3/2mr^2`

D

`2mr^2`

Text Solution

Verified by Experts

The correct Answer is:
C

Moment of inertia of a ring about its axis is, `I_2 = mr^2`
Moment of inertia of a ring about an axis passing through the center and lying in its plane is, `I_1 = (mr^2)/2`
We know that `I_1 = I_1 + I_2`
`implies I = (mr^2)/2 + mr^2`
`implies I =3/2 mr^2`
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Knowledge Check

  • Two rings of same radius and mass m are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to plane of one of the rings is

    A
    `(1)/(2)mr^(2)`
    B
    `mr^(2)`
    C
    `(3)/(2)mr^(2)`
    D
    `2mr^(2)`

  • Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring = m, radius = r)

    A
    `(1)/(2) mr^(2)`
    B
    `mr^(2)`
    C
    `(3)/(2) mr^2`
    D
    `2mr^2`

  • Two rings of the same radius R and M are placed such that their centres coincide and their planes are perpendicular to each other, the moment of inertia of the system about an axis passing through the diameters of both rings is

    A
    `(MR^(2))/4`
    B
    `(MR^(2))/2`
    C
    `(3MR^(2))/4`
    D
    `MR^(2)`

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