A pendulum bob is made of a ball filled with water. What would happen to the frequency of vibration of this pendulum if a hole in the ball allowed water to slowly leak out? (Treat the pendulum as a simple pendulum).

Frequency will not change.

Explanation:

As you know, Time period 'T' = 2π x √(L/g)

where,

L= the length of the pendulum

g=  acceleration due to gravity

and Frequency 'f' is the reciprocal of period.f=1/T

From above, we can conclude that frequency is not dependent on mass.

It depends upon the acceleration due to gravity 'g' and the length of the pendulum 'L'

So, if a hole in the ball allowed water to slowly leak out, frequency would not change

true tan speed = ang vel x radius