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(a) Find the moment of inertia of a sphe...

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of interia of the sphere about any of its diameter 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 diameter to be -`(1)/(4)MR^(2)`, find the moment of inertia about an axis normal to the dise passing through a point on its edge.

Text Solution

Verified by Experts

(a)`(7)/(5)MR^(2)` and (b)`(3)/(2)MR^(2)`
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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 2MR^(2)//5 . Where M is the mass of the sphere and R is the radius of the sphere.

(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 2MR^(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 MR^(2)//4 , find its moment of inertia about an axis normal to the disc and passing through a point on its edge.

Knowledge Check

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

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

  • The radius of gyration of a hollow sphere about a tangent is

    A
    `R sqrt(7//5)`
    B
    `R sqrt(2//5)`
    C
    `R sqrt(2//3)`
    D
    `R sqrt((5)/(3))`

  • The radius of gyration of a hollow sphere about a tangent is

    A
    `Rsqrt((7)//5))`
    B
    `Rsqrt((2)//(5))`
    C
    `Rsqrt((2)/(3))`
    D
    `Rsqrt((5)/(3))`

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