An object is released from rest. A pendulum clock is utilized to...

The actual time of fall is given by $t = \sqrt{\dfrac{2h}{g}}$.

The time period of a pendulum clock is $T = 2\pi\sqrt{\dfrac{L}{g}}$.

The measured time is proportional to the number of oscillations the pendulum makes during the fall, which is $n = \dfrac{t}{T} = \dfrac{1}{2\pi}\sqrt{\dfrac{2h}{L}}$.

Since $n$ is independent of the acceleration due to gravity $g$, the measured times are identical on the Earth and the Moon.

The actual speed of the object after falling a distance $h$ is $v = \sqrt{2gh}$, which depends on $g$. Thus, the actual speeds are different.

The measured speed is calculated using the measured time. Since the measured time and the distance $h$ are identical in both cases, the measured speeds are also identical.