7.10 (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.

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Vishal Baghel | Contributor-Level 10

4 months ago

(a)

The moment of Inertia of a sphere about its diameter = 2MR ²/5

According to the theorem of parallel axis, 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 square of the distance between two parallel axes

Hence the moment of inertia about a tangent of the sphere = 2MR ²/5 + MR² = 7MR ²/5

(b)

The moment of inertia of a disc about its diameter = MR ²/4

According to the theorem of perpendicular axis, the moment of inertia of a planar body about an axis perpendicular to its plane is equal to t

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