Question
A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius 𝑟 and outer radius 𝑅 are such that 𝑟2 = 𝑅2/2, and the acceleration due to gravity is 𝑔. If the time period of small amplitude simple harmonic motion is given by T= ßπ√(R/g), where 𝜋 is the ratio of circumference to diameter of a circle, then 𝛽= ________ (round off to 2 decimal places).
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