Two wheels A and C are connected by a belt B as shown in figure. The radius of C is three times the radius of A. What would be the ratio of the rotational inertias IC/IA if both the wheels have the same rotational kinetic energy?

As the belt does not slip, vP=vQi.e., rAωA=rCωC  [ as v=rω]              …(i)According to the given problem if rA=r, rC=3r, so Eq. (i) becomesωA=3ωC                      …(ii)If both the wheels have the same rotational kinetic energy, then12IAωA2=12ICωC2IAIC=ωCωA2=132=19