First slide

Moment of intertia

Question

A solid sphere of radius R is rotating about an axis passing through its centre with a time period 0.5 seconds. During the rotation, if the sphere suddenly changes into a solid cylinder of height $\frac{R}{3}$ such that axis of cylinder coincides with axis of rotation, the time period of rotation of cylinder is

Moderate

Solution

$\begin{array}{l} I ω = I \times \frac{2 π}{T} = constant \\ T \propto Ι \\ \frac{I_{1}}{I_{2}} = \frac{(2 / 5) R^{2}}{R_{2}^{2} / 2} and \frac{4}{3} π R^{3} = π R_{2}^{2} \times \frac{R}{3} \Rightarrow R_{2} = 2 R \\ ∴ \frac{T_{1}}{T_{2}} = \frac{1}{5} \Rightarrow T_{2} = 2.5 \sec \end{array}$

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