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)  51                                         

B)  31

C)  41                                         

D)  61

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                 \[\frac{I}{I}=\frac{3}{2}M{{R}^{2}}\times \frac{4}{M{{R}^{2}}}=6\] \[\Rightarrow \]               \[I=6I\]