A pendulum clock becomes

Options

A. slower in winter
B. faster in summer
C. slower in summer and faster in winter
D. nothing can be decided

Answer

To solve the question regarding how a pendulum clock behaves in different seasons, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Understanding the Pendulum Clock**:
A pendulum clock operates based on the principle of a pendulum's motion, where the time period (T) of the pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity.

2. **Effect of Temperature on Length**:
- In winter, the temperature is lower. Generally, materials contract in colder temperatures, which means that the length \(L\) of the pendulum will decrease.
- In summer, the temperature is higher, causing materials to expand, which means that the length \(L\) of the pendulum will increase.

3. **Analyzing the Time Period**:
- When the length \(L\) decreases (as in winter), the time period \(T\) will also decrease because \(T\) is directly proportional to the square root of \(L\). This means the pendulum will swing faster, and the clock will run faster.
- Conversely, when the length \(L\) increases (as in summer), the time period \(T\) will increase, meaning the pendulum will swing slower, and the clock will run slower.

4. **Conclusion**:
- Therefore, in winter, the pendulum clock becomes faster due to the decrease in length, and in summer, it becomes slower due to the increase in length.
- The correct answer is: **The pendulum clock is slower in summer and faster in winter**. This corresponds to **Option 3**.

### Final Answer:
The correct option is **Option 3: Slower in summer and faster in winter**.

---