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Finding the Ratio of Final Period to Initial Period

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A uniform sphere, mass M= 84 kg, radius R, has two uniform, thin, flexible bars each with mass m= 25 kg, and length half a circumference, wrapped on its surface as shown in Fig. 1. The system is rotating with a period To about a c.m. axis at center. At some instant, the bars fly outward to form a new configuration shown in Fig. 2.
Find the ratio of the final period Tf to the initial period To.

See attachment for a diagram of the system.

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Provides steps necessary to find the ratio of the final period Tf to the initial period To.

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