question_answer

Moment of inertia of a circular wire of mass M and radius R about its diameter is                     [AIEEE 2002]

A)   \[M{{R}^{2}}/2\]

B)                   \[M{{R}^{2}}\]

C)     \[2M{{R}^{2}}\]       

D)        \[M{{R}^{2}}/4\]

Correct Answer: A

Solution :

[a] Moment of inertia of circular wire about its axis is \[M{{R}^{2}}\]. Consider two diameters \[XX'\] and \[YY'\] moment of inertia about any of this diameter is same let us say \[l\].

From perpendicular axis theorem,

\[l+l=M{{R}^{2}}\]

\[l=\frac{M{{R}^{2}}}{2}\]