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Question
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 2MR2/5, where M is the mass of the sphere and R is the radius of the sphere.
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Solution 1
`7/5 MR^2`
The moment of inertia (M.I.) of a sphere about its diameter = `2/5 MR^2`
`ML = 2/5MR^2`
According to the theorem of parallel axes, the moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.
The M.I. about a tangent of the sphere = `2/5 MR^2 + MR^2 = 7/5 MR^2`
Solution 2
Moment of inertia of sphere about any diameter = 2/5 MR2
Applying theorem of parallel axes, Moment of inertia of sphere about a tangent to the sphere = 2/5MR2 +M(R)2 =7/5 MR2
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