Question

Two circle loops A and B of radii R and 2R respectively are made of the similar wire . Ratio of their moments of inertia about the axis passing through the centre perpendicular to their planes will be

Answer 1

Moment of inertia of a circular ring about its centre and perpendicular to plane is given by:-

$I_C=M{R}^2$

$I_C\propto R^2$

So ratio of $I_c$ for loops A and B:-

$\frac{T_{c_1}}{I_{C_2}}=\frac{R_A^2}{R_B^2}=\frac{R^2}{(2R{)}^2}=\frac{1}{4}$