Two identical rods each of mass m and length ℓ , are rigidly joined and then suspended in a vertical plane so as to oscillate freely about an axis normal to the plane of paper passing through ' S

Question

Two identical rods each of mass m and length ℓ , are rigidly joined and then suspended in a vertical plane so as to oscillate freely about an axis normal to the plane of paper passing through ' S ' (point of suspension). Time period of such small oscillations = 3 2 π ​ β g α ℓ ​ ​ , then find the value of ( α + β ) .

TestHub · Accepted Answer

Compute the moment of inertia of the joined rods about S and the distance of the combined centre of mass from S.

$T = 2 π I / m_{tot} g d$

Matching with $\frac{2 π}{3} α ℓ / β g$ gives least integers with $α + β = 19$ .

Answer: 19.00

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