Two thin circular rings are lying in the same plane and are touching each other at a single point. The first ring has mass 5 kg and radius 10 cm , while the second ring has mass 10 kg and radius 20 cm . Find the moment of inertia of the combined system about a straight line passing through the point of contact and lying in the plane of the rings. (A) $\frac { 27 } { 50 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$ (B) $\frac { 24 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$ (C) $\frac { 27 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$ (D) $\frac { 17 } { 12 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
Two thin circular rings are lying in the same plane and are touching each other at a single point. The first ring has mass 5 kg and radius 10 cm , while the second ring has mass 10 kg and radius 20 cm . Find the moment of inertia of the combined system about a straight line passing through the point of contact and lying in the plane of the rings.
(A) $\frac { 27 } { 50 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(B) $\frac { 24 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(C) $\frac { 27 } { 40 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$
(D) $\frac { 17 } { 12 } \mathrm {~kg} \mathrm {~m} ^ { 2 }$