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.

Find the moment of inertia of a sphere about a tangent to the sphere.

1.	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.
Answer» Solution :The centre of mass (cm) of the sphere is on its diameter AB Fig .`I_(cm)=(2)/(5) "MR"^(2)` ACCORDING to the parallel-axes theorem the MOMENT of inertia of the sphere about the tangent CD, `I=I_(cm)+MR^(2)=(2)/(5)MR^(2)+MR^(2)=(7)/(5)MR^(2)`