question_answer

Find the ratio of moment inertia of a ring about an axis passing through the circumference and perpendicular to the plane to the moment inertia about its diameter:

A)  1 : 4                      

B)         4 : 1  

C)  1 : 2                      

D)         2 : 1

Correct Answer: C

Solution :

Moment of inertia of ring \[I=m{{r}^{2}}\] Moment of inertia of ring about diameter (front theorem of parallel axis)                 \[{{I}_{1}}=m{{r}^{2}}+m{{r}^{2}}=m{{r}^{2}}\]                 \[I:={{I}_{2}}=1:2\]