Question

A thin rod of length l and mass m oscillating about its one end

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The time period of oscillation of a uniform rod with length l pivoted at one end is

2πl2g−−−√2πlg−−√2π2l3g−−−√2πl3g−−−√

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A)

Solution :

For a rigid body oscillating about horizontal axis passing through the point O the time period is given by

T=2πImg(OG)−−−−−−−√

Where I moment of rigid body and OG is the distance of the point of pivot to the centre of gravity G and I is the moment of inertia of the rod.

I=13me2

OG=l2

T=2π13ml2mgl2−−−−−−⎷

=2π2l3g−−−√

Answer : 2π2l3g−−−√