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Find the moment of inertia of a uniform ...

Find the moment of inertia of a uniform sphere of mass m and radius R about a tangent if the spheres (1) solid (ii) hollow?

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To find the moment of inertia of a uniform sphere about a tangent, we will consider both a solid sphere and a hollow sphere. We will use the parallel axis theorem for this calculation. ### Step-by-Step Solution: **Step 1: Moment of Inertia of Solid Sphere about its Center of Mass** - The moment of inertia \( I_{cm} \) of a solid sphere about an axis through its center of mass is given by: \[ I_{cm} = \frac{2}{5} m R^2 ...
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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 inertia of a solid sphere of density p and radius R about its diameter is

    A
    `(176piR^(3))/105`
    B
    `(176pR^(5))/105`
    C
    `(105pR^(3))/176`
    D
    `(105pR^(5))/176`
  • The M.I. of a solid sphere of mass 'M' and radius 'R' about a tangent in its plane is

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