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Find the moment of inertia of a sphere a...

Find the moment of inertia of a sphere about a tangent to the sphere, while the mass of the sphere is M and the radius of the sphere is R.

Text Solution

Verified by Experts

The moment of inertia of a sphere about its
own axis (YY') is `(2MR^(2))/(5)`
Applying the throrem of parallel axes the moment of inertia of the sphere about tangent `(XX')`
`I_(t) = I+MR^(2)`
`I_(t)=(2)/(5)MR^(2)+MR^(2)=(7)/(5)MR^(2)`
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(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2 MR^(2)//5, where M is the mass of the sphere and R is the radius of the sphere. (b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be (1)/(4)MR^(2) , find the moment of inertia about an axis normal to the disc passing through a point on its edge.

What is moment of inertia of a solid sphere about its diameter ?

Knowledge Check

  • The moment of inertia of a solid sphere of mass ‘M' and radius 'R' about a tangent to the sphere is

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

  • The moment of ineria (I) of a sphere of radius R and mass M is given by

    A
    `I=MR^(2)`
    B
    `I=(1//2)MR^(2)`
    C
    `I=(4//3)MR^(2)`
    D
    `I=(2//5)MR^(2)`

  • Two spheres of same mass and radius are in contact with each other. If the moment of inertia of a sphere about its diameter is I, then the moment of inertia of both the spheres about the tangent at their common point would be

    A
    3I
    B
    7I
    C
    4I
    D
    5I

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