Question

A uniform solid cylinder with radius $R$ and length $L$ has moment of inertia $I _1$, about the axis of the cylinder A concentric solid cylinder of radius $R^{\prime}=\frac{R}{2}$ and length $L^{\prime}=\frac{L}{2}$ is carved out of the original cylinder. If $I _2$ is the moment of inertia of the carved out portion of the cylinder then $\frac{I_1}{I_2}$ $=$_______ (Both $I _1$ and $I _2$ are about the axis of the cylinder)

Answer 1

The correct answer is 32.

I1​=2m1​R2​I2​=2m2​(R/2)2​
I2​I1​​=m2​4m1​​=ρ⋅4πR2​×2ℓ​4⋅ρπR2ℓ​⇒I2​I1​​=32