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A uniform meter stickis suspended throug...

A uniform meter stickis suspended through a small pin hole at the 10 cm mark. Find the time period of small oscillation about the point of suspension.

Text Solution

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Let the mass of the stick be m. The moent of inertia of the stick about the axis of rotation through the point of suspension is
`I=(ml^2)/12+md^2, `
where l=1 m and d=40cm

The seperation between the centre of mass of the stick and the point of suspension is d=40 cm. The time period of this physical pendulum is
`T=2pi sqrt(I/(mgd))`
`=2pi sqrt(((ml^2)/12+md^2)/(mgd))`
`=2pi[sqrt(1/12+0.16)/4])s=1.55s`
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