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A circular hole of radius R/4 is made in athin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is:
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A circular hole of radius R/4is made in athin uniform disc having mass...
Let the mass per unit area of disc be σ 

Now, moment of inertia of removed mass

 (M2​)=⎛2(σA′)(4R​)2​+(σA′)(43R​)2⎠


Using parallel axis theorem

M2​=(σA′)(32R2​+169R2​)

A′=π(4R​)2=16πR2​

M2​=(16σπR4​)(3219​)


Also, moment of inertia of complete disc is:

⇒M1​=(2(σA)×R2​)


Effect moment of inertia = M1​−M2​

M0​=2σ​πR4−512σπR4.19​

M0​=(σπR2).R2.512237​

σπR2=M
M0=237/512MR2
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A circular hole of radius R/4is made in athin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is:a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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