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For the same total mass which of the fol...

For the same total mass which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body.

A

a disc of radius a

B

a ring of radius oa

C

a square lamina of side `2 a`

D

four rods forming a square of side `2a`.

Text Solution

Verified by Experts

The correct Answer is:
D
For Disc `I_("disc") = (1)/(2) ma^(2)`
For Ring `I_("ring") = ma^(2)`
For square lamine of side `2a = (1)/(6) m(2a)^(2) = (2)/(3) ma^(2)`

For Rods forming a square of side `2 a`
`I_("square") = 4[(m(2a)^(2))/(12) +ma^(2)] =4[(ma^(2))/(3)+ma^(2)] = (16 ma^(2))/(3)`.
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Knowledge Check

  • For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the body

    A
    a disc of radius R
    B
    a ring of radius R
    C
    a square lamina of side 2 R
    D
    four rods forming a square of side 2R

  • For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the of body?

    A
    a ring o radius `l`
    B
    a disc of radius `l`
    C
    a square lamina of side `2l`
    D
    Four rods forming square of side `2l`

  • Moment of inertia of a circular ring about an axis through its centre and perpendicular to its plane is

    A
    `I = (1)/(2) MR^2`
    B
    `I = MR^2`
    C
    `I = (3)/(2) MR^2`
    D
    `I = (5)/(2) MR^2`

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