The time period of a pendulum is given as:
`T = 2pi sqrt(L/g)`
where, T is the time period, L is the length of the pendulum and g is acceleration due to gravity. In this equation, length is the independent variable, while the time period is the dependent variable.
When we change the length (case A) of the pendulum, time period changes. A change in mass of the pendulum does not have any effect on the period of the pendulum. When we change both the length and the mass (case B), time period changes.
A fixed variable or a control variable is one which stays constant throughout. In both the given cases, acceleration due to gravity (g) stays constant. In the experiments that we carry out to study pendulum, we generally study the effect of variations in length, mass and angle of pendulum. In all those cases, g is constant and hence is the fixed variable. Specifically for the case, when we change only the mass of pendulum bob, length is also kept constant or fixed.
Hope this helps.