question_answer

Moment of inertia of a uniform disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

A)  \[5I\]            

B)  \[3I\]

C)  \[4I\]           

D)  \[6I\]

Correct Answer: D

Solution :

From theorem of parallel axis \[I'=M{{R}^{2}}+{{I}_{0}}\] Where \[{{I}_{0}}\] is moment of inertia through axis. Given, \[{{I}_{0}}=\frac{M{{R}^{2}}}{2}\] \[\therefore \] \[I'=M{{R}^{2}}+\frac{M{{R}^{2}}}{2}=\frac{3}{2}M{{R}^{2}}\] ?..(i) Also, moment of inertia of disc about a diameter is \[I=\frac{M{{R}^{2}}}{4}\] ?.(ii) From Eqs. (i) and (ii), we get \[\frac{r}{I}=\frac{3}{2}M{{R}^{2}}\times \frac{4}{M{{R}^{2}}}=6\] \[\Rightarrow \] \[I'=6I\]