A wall clock uses a vertical spring mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives correct time at the equator. If the clock is taken to the poles it will

Options

A. run slow
B. run fast
C. stop working
D. give correct time

Answer

To solve the problem, we need to analyze how the wall clock, which uses a vertical spring-mass system, functions at different locations on Earth, specifically at the equator and the poles.

### Step-by-Step Solution:

1. **Understanding the Spring-Mass System**:
The time period \( T \) of a spring-mass system is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where \( m \) is the mass attached to the spring and \( k \) is the spring constant.

2. **Time Period at the Equator**:
The clock is designed to advance by one second each time the mass reaches an extreme position. Therefore, the time period for the clock is:
\[ T = 2 \text{ seconds} \]
This is because it takes one second to reach one extreme position and another second to return to the other extreme position.

3. **Effect of Gravity**:
The time period of a spring-mass system does not depend on the acceleration due to gravity \( g \). This is because the formula for the time period does not include \( g \). Thus, the time period remains constant regardless of the location.

4. **Comparison of Gravity at the Equator and Poles**:
At the equator, the value of \( g \) is slightly less than at the poles due to the Earth's rotation and its shape. However, since the time period of the spring-mass system does not depend on \( g \), the clock's mechanism will not be affected by this difference.

5. **Conclusion**:
Since the clock gives the correct time at the equator and the time period remains unchanged when taken to the poles, the clock will continue to give the correct time at the poles as well.

### Final Answer:
The clock will give the correct time at the poles.