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What is the period of a pendulum formed ...

What is the period of a pendulum formed by pivoting a metre stick so that is free to rotate about a horizontal axis passing through the `75 cm` mark?

Text Solution

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Let `m` be the mass and l be the length of the stick
`l = 100 cm`
The distance of the point of suspension from center of gravity is `d = 25 cm`
Moment of inertia about a horizontal axis through O is
`l = l_(C) + m d^(2) implies (ml^(2))/(12) + m d^(2)`
` implies T = 2 pi sqrt((l)/(mgd)) = 2 pi sqrt(((ml^(2))/(12) + md^(2))/(mgd))`
`implies T = 2 pi sqrt((l^(2) + 12 d^(2))/(12 gd)) = 2 pi sqrt ((l^(2) + 12 (0.25)^(2))/(12 xx 9.8 xx 0.25)) = 153 s`
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