Classical Mechanics Level 5

Consider 2 similar Rods of mass \(M\) and length \(L\).Their cross-sectional area is \(A\) and Young's Modulus is \(Y\) .They are in the following conditions.

\( Rod - 1 :\) It is hinged at one end and is rotating in the horizontal plane with constant angular velocity \(\omega\).

Its Elastic Potential Energy is \( {U}_{1} = \frac{M^2 \omega^4 L^3}{a A Y}\)

\( Rod - 2 :\) It is hanging freely (through its one end) from ceiling

Its Elastic Potential Energy is \( {U}_{2} = \frac{M^2 g^2 L}{b A Y}\)

where \(a\) & \(b\) are positive integers

Enter your answer as \(\frac{a}{b}\)

This is a part of my set Aniket's Mechanics Challenges.

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