question_answer

The moment of inertia of uniform semi-circular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is     AIEEE  Solved  Paper-2005

A) \[\frac{1}{4}M{{r}^{2}}\]    

B)                        \[\frac{2}{5}M{{r}^{2}}\]              

C)        \[M{{r}^{2}}\]        

D)                        \[\frac{1}{2}M{{r}^{2}}\]

Correct Answer: D

Solution :

The mass of complete (circular) disc is The moment of inertia of disc about the given axis is \[l=\frac{2M{{r}^{2}}}{2}=M{{r}^{2}}\] The disc may be assumed as combination of two semi-circular parts. Thus, the moment of inertia of a semi-circular part of disc, \[{{l}_{1}}-l-{{l}_{1}}\] \[{{l}_{1}}=\frac{l}{2}=\frac{M{{r}^{2}}}{2}\]