Two rings have their moments of inertia in the ratio 4 : 1 and their diameters are in the ratio 4 : 1. Find the ratio of their masses.1 : 22 : 14 : 11 : 4
Question
Two rings have their moments of inertia in the ratio 4 : 1 and their diameters are in the ratio 4 : 1. Find the ratio of their masses.1 : 22 : 14 : 11 : 4
Solution
The moment of inertia (I) of a ring is given by the formula I = m*r^2, where m is the mass of the ring and r is the radius.
Given that the moments of inertia of the two rings are in the ratio 4 : 1, we can write this as I1/I2 = 4/1.
Also given that the diameters of the two rings are in the ratio 4 : 1, the radii of the rings will also be in the ratio 4 : 1. We can write this as r1/r2 = 4/1.
Substituting these ratios into the formula for the moment of inertia, we get:
(m1r1^2) / (m2r2^2) = 4/1 (m1*(4r2)^2) / (m2r2^2) = 4/1 (m116) / m2 = 4/1 m1/m2 = 4/16 = 1/4
So, the ratio of the masses of the two rings is 1 : 4.
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