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Find the moment of inertia of a hemisphe...

Find the moment of inertia of a hemisphere of mass `M` and radius `R` shown in the figure, about an axis `A A'` tangential to the hemisphere.

A

`I=(9/20)mR^(2)`

B

`I=(13/20)mR^(2)`

C

`I=(7/20)mR^(2)`

D

`I=(3/20)mR^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Moment of inertia about an axis through the flat face of hemisphere

`I_(0)=2/5 mR^(2)`
From the parallel axis theoram, the moment of inertial through c.m. of the hemisphere
`I_(0)=I_(0)-m(3/8R)^(2)=(83/320)mR^(2)`
Using parallel axis theoram, moment of inertia about the axis `A A'`,
`I=I_(G)+m(5/8R)^(2)rArrI=(13/20)mR^(2)`
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Knowledge Check

  • Moment of inertia of a disc of mass 'M' and radius 'R' about the diameter is

    A
    `(MR^2)/(2)`
    B
    `(MR^2)/(4)`
    C
    `(MR^2)/(3)`
    D
    `(MR^2)/(12)`

  • Find the moment of inertia of a solid sphere of mass M and radias R about an axis XX shown in figure. Also find radius of gyration about the given axis.

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

  • Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is

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

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