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## Homework Statement

A uniform rod of mass m and length L is freely pivoted at one end. What is the period of its oscillations? I

_{cm}for a uniform rod rotating about its centre of mass is 1/12mL

^{2}

(a) √3g/2L

(b) 2π √3L/2g

(c) 2π √2L/3g

(d) 2π √L/g

(e) none of the above

## Homework Equations

ω

^{2}= mgL/I

I

_{cm}= 1/12mL

^{2}

I = I

_{cm}+1/12mL

^{2}

Period: T = 2π/ω

## The Attempt at a Solution

I'm fairly certain that the answer is "none of the above", but I'd just like to make sure I'm not neglecting anything in what seems to be a simple plug-and-chug question.

I = I

_{cm}+1/12mL

^{2}= 1/12mL

^{2}+ mL

^{2}= 13/12 mL

^{2}

ω = √mgL/I= √(mgL)/(13/12)mL

^{2}= √12g/13L

T = 2π/ω = 2π √13L/12g

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