Question

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at its bottom, the period of oscillation will.

Answer 1

The period wlll decrease - it will swing faster

The period of a simple pendulum is just

P = 2 π √(L / g)

However, with a compound pendulum one must also consider the moment of inertia about the center of mass at distance L.

As water drains from the sphere its moment of inertia about its point of suspension will decrease and the pendulum will swing faster

Technically P = 2 π √I0 / M g L)

where I0 = M L^2 + Icm Icm is moment of inertia about the center of mass - if Icm = zero then P = 2 π √(L / g) the simple pendulum