J & K CET Medical
J & K - CET Medical 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) 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 \[\frac{I}{I}=\frac{3}{2}M{{R}^{2}}\times \frac{4}{M{{R}^{2}}}=6\] \[\Rightarrow \] \[I=6I\]