# Elasticity

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 $$\frac{a}{b}$$

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