Object #1 is a \"donut\" with a mass of M , a radius of R , and a hole of radius

Question

Object #1 is a "donut" with a mass of M, a radius of R, and a hole of radius R/2.
Object #2 is a solid disk with the same total weight and radius, but no hole.

Which of the following is true?

(A)These objects have the same moment of inertia

(B)Object #2 has a larger moment of inertia   

(C)Object #1 has a larger moment of inertia

(D)There is not enough information to tell

#Please explain why you made the choice you did.

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Explanation / Answer

Here ,

both the object have same weight , hence same mass ,

as the moment of inertia of a point mass is given as I = M * r^2

where r is the distance of mass from the axis

For object 1 , as overall mass is more distant than on the object 2

the moment of inertia of #1 is larger

(C)Object #1 has a larger moment of inertia

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