question_answer

The moment of inertia of disc about a tangent axis in its plane is

A) \[\frac{M{{R}^{2}}}{4}\]        

B)        \[\frac{3M{{R}^{2}}}{2}\]

C) \[\frac{5}{4}M{{R}^{2}}\]      

D)        \[\frac{7M{{R}^{2}}}{4}\]

Correct Answer: C

Solution :

[c] Moment of inertia of a disc about a diameter \[=\frac{1}{2}\times \frac{1}{2}M{{R}^{2}}=\frac{1}{4}M{{R}^{2}}\] \[[{{I}_{x}}+{{I}_{y}}={{I}_{z}}=\frac{1}{2}M{{R}^{2}}]\] Applying theorem of parallel axis.             \[{{I}_{z}}=\frac{1}{4}M{{R}^{2}}+M{{R}^{2}}=\frac{5}{4}M{{R}^{2}}\]