A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is π$$B2Rg$$. The value of B is $$_______$$.

Question

A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is π$$B2Rg$$. The value of B is $$_______$$.

Infinity Learn · Accepted Answer

The time period of a physical pendulum (or compound pendulum) is minimum when the distance between point of suspension and COM (i.e. l) is equal to the radius of gyration about its COM i.e. l = k.

The moment of inertia of a disc about an axis perpendicular to its plane and passing through its COM is

$\begin{array}{l} I = {mk}^{2} = \frac{1}{2} {mR}^{2} \Rightarrow k = \frac{R}{\sqrt{2}} \\ T = 2 π \sqrt{\frac{m (k^{2} + l^{2})}{mgl}} \\ \Rightarrow T_{min} = 2 π \sqrt{\frac{\frac{R^{2}}{2} + \frac{R^{2}}{2}}{gR / \sqrt{2}}} \Rightarrow T_{min} = 2 π \sqrt{\frac{\sqrt{2} R}{g}} = π \sqrt{\frac{4 \sqrt{2} R}{g}} \\ \Rightarrow B = 4 \end{array}$

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A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is $π \sqrt{\frac{B \sqrt{2 R}}{g}}$ . The value of B is _______.

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Applications of SHM

Remember concepts with our Masterclasses.

A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is πB2Rg. The value of B is _______.

Ready to Test Your Skills?

free study material

A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is $π \sqrt{\frac{B \sqrt{2 R}}{g}}$ . The value of B is _______.