Q.

Given a uniform disc of mass M and radius R. A small disc of radius R/2 is cut from this disc in such a way that the distance between the centers of the two discs is R/2. Find the moment of inertia of the remaining disc about a diameter of the original disc perpendicular to the line connecting the centers of the two discs.

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a

3MR2/32

b

5MR2/16

c

11MR2/64

d

None of these

answer is C.

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Detailed Solution

Mass of cut disc: m1=M/4Moment of inertia of original disc about axis 1:I=14MR2Moment of Inertia of small disc about axis 1:I′=14m1R22+m1R22 or I′=516m1R2=564MR2 Required moment of inertia: I−I′=14MR2−564MR2=1164MR2
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Given a uniform disc of mass M and radius R. A small disc of radius R/2 is cut from this disc in such a way that the distance between the centers of the two discs is R/2. Find the moment of inertia of the remaining disc about a diameter of the original disc perpendicular to the line connecting the centers of the two discs.