A uniform rod of mass m and length l₀ is pivoted at one end and is hanging in the vertical direction. The period of small angular oscillations of the rod is

Step-by-step solution

Here, the rod is oscillating about an end point O . Hence, moment of inertia of rod about the point of oscillating is I = 1 3 ~m l₀^2 Moreover, length l of the pendulum = distance from the oscillation axis to centre of mass of rod =l₀ / 2 Time period of oscillation, aligned & T =2 I mg l =2 l 3 ~m l₀^2 m g ( l₀ 2 ) & T =2 2 l₀ 3 ~g & aligned