Question

A string of simple pendulum is replaced by a thin uniform rod of mass 2m and length l then the te period of oscillation

Answer 1

Solution :

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

T=2πImg(OG)−−−−−−−√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=13I=13me2me2

OG=l2OG=l2

T=2π13ml2mgl2−−−−−−⎷T=2π13ml2mgl2

=2π2l3g−−−√=2π2l3g

Answer : 2π2l3g−−−√