Ball a, of mass m_{a}, is connected to ball b, of mass m_{b}, by a massless rod of length L. The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes *a* and *b*. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-mass system about axis *a* I_{a}, and the moment of inertia of the system about axis *b* is I_{b} It is observed that the ratio of I_{a} to I_{b} is equal to 3:

(a) Assume that both balls are point-like; that is, neither has any moment of inertia about its own center of mass. Q. Find the ratio of the masses of the two balls.

= ?

(b) Find d_{a}, the distance from ball A to the system's center of mass.

(Express your answer in terms of L ,the length of the rod.)