A cylindrical solid of mass M has radius R and length L. Its mome…

MCQ

A cylindrical solid of mass $M$ has radius $R$ and length $L$. Its moment of inertia about a generator is:

A
$\text{M}\Big(\frac{1}{2\text{R}}+\frac{\text{R}^2}{4}\Big)$
B
$\text{M}\Big(\frac{\text{L}}{3}+\frac{\text{R}^2}{4}\Big)$
C
$\frac{1}{2}\text{MR}^2$
✓
$\frac{3}{2}\text{MR}^2$

✓

Answer

Correct option: D.

$\frac{3}{2}\text{MR}^2$

Generator is axis touching surface of cylinder and parallel to axis of cylinder. Using theorem of parallel axis,
$\text{I}=\text{I}_0+\text{MR}^2=\frac{1}{2}\text{MR}^2+\text{MR}^2$
$\text{I}=\frac{3}{2}\text{MR}^2$

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