A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached to the end opposite the pivot. This arrangement is a good approximation to a simple pendulum (period = 5.97 s), because the mass of the sphere (lead) is much greater than the mass of the rod (aluminum). When the sphere is removed, the pendulum is no longer a simple pendulum, but is then a physical pendulum. What is the period of the physical pendulum?

To calculate the period of a physical pendulum, we need to consider the moment of inertia of the system and its distance from the axis of rotation. In this case, the moment of inertia changes when the sphere is removed.

For a simple pendulum, the formula to calculate the period is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Now, in the case of a physical pendulum, the formula becomes T = 2π√(I/mgd), where I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance between the pivot point and the center of mass of the pendulum.

When the sphere is removed, the mass of the pendulum becomes only the mass of the rod (aluminum), and the moment of inertia changes as well. The moment of inertia for a thin rod rotating about one end (pivot) is given by I = (1/3)ml^2, where m is the mass of the rod and l is its length.

To find the period of the physical pendulum, we need to know the length of the rod. Unfortunately, this information is missing from the question. Once we have the length, we can substitute the values into the formula T = 2π√(I/mgd) to find the period of the physical pendulum.

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