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

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.