question_answer

A solid cylinder has mass M, length L and radius R. The moment of inertia of this cylinder about a generator is

A)  \[M\left( \frac{{{L}^{2}}}{12}+\frac{{{R}^{2}}}{4} \right)\]

B)  \[\frac{M{{L}^{2}}}{4}\]

C)  \[\frac{1}{2}M{{R}^{2}}\]

D)  \[\frac{3}{2}M{{R}^{2}}\]

Correct Answer: B

Solution :

 Generator axis of a cylinder is a line lying on it's surface and parallel to axis of cylinder By parallel axis theorem      \[I=\frac{M{{R}^{2}}}{2}+M{{R}^{2}}\] \[I=\frac{3}{2}M{{R}^{2}}\]