Ball a, of mass m a , is connected to ball b, of mass m b , by a massless rod of

Question

Ball a, of mass ma, is connected to ball b, of mass mb, 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 is Ia, and the moment of inertia of the system about axis b is Ib. It is observed that the ratio of Ia to Ib is equal to 3:

Ia/Ib=3

Find the ratio of the masses of the two balls.

Assume that both balls are pointlike; that is, neither has any moment of inertia about its own center of mass.

Explanation / Answer

from axis a:
moment of inertia, Ia = mb*L^2

from axis b:
moment of inertia, Ib = ma*L^2

Ia/Ib = (mb*L^2) / (ma*L^2) = mb/ma
so,
mb/ma = Ia/Ib = 3
Answer:
ma/mb = 1/3

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