Question

A pendulum clock is running fast. To correct its time, we should

• A. reduce the mass of the bob.
• B. reduce the amplitude of oscillation.
• C. increase the length of the pendulum.
• D. reduce the length of the pendulum.

Hint:

Remember this straightforward mnemonic rule for pendulum clock maintenance:
Running FAST $\rightarrow$ Needs to slow down $\rightarrow$ INCREASE length ($\uparrow l$).
Running SLOW $\rightarrow$ Needs to speed up $\rightarrow$ DECREASE length ($\downarrow l$).

Answer 1

The Correct Option is C

Step 1: Understand the problem.
A pendulum clock is running fast. That means each swing takes too little time, so the clock shows a time ahead of the real time. To fix it we must make each swing take longer.
Step 2: The time period formula.
For a simple pendulum the time of one swing is \[ T = 2\pi\sqrt{\frac{l}{g}} \] Here $l$ is the length of the pendulum and $g$ is gravity.
Step 3: What T depends on.
From the formula, $T \propto \sqrt{l}$. The period grows when the length grows. It does not depend on the mass of the bob or on how wide it swings.
Step 4: Rule out wrong choices.
Changing the bob mass does nothing to $T$. Changing the swing size (amplitude) also does nothing. So those options cannot correct the clock.
Step 5: Pick the correct change.
A fast clock needs a larger period, so we must increase the length of the pendulum. A shorter length would make it run even faster, which is wrong.
Step 6: State the answer.
We should increase the length of the pendulum, which is option (3). \[ \boxed{\text{Increase the length of the pendulum}} \]