J & K CET Engineering
J and K - CET Engineering Solved Paper-2003
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 \[\frac{r}{I}=\frac{3}{2}M{{R}^{2}}\times \frac{4}{M{{R}^{2}}}=6\] \[\Rightarrow \] \[I'=6I\]