Time period of oscillation of a spring is 12 s on earth. What shall be the time period if it is taken to moon?

Options

A. 6 s
B. 12 s
C. 36 s
D. 72 s

Explanation

To solve the problem, we need to understand how the time period of a spring-mass system is determined and whether it changes when the system is taken from Earth to the Moon.

### Step-by-step Solution:

1. **Understand the Formula for Time Period**:
The time period \( T \) of a spring-mass system is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where:
- \( T \) is the time period,
- \( m \) is the mass attached to the spring,
- \( k \) is the spring constant.

2. **Identify the Variables**:
In this case, we know:
- The time period on Earth \( T = 12 \, \text{s} \).
- The mass \( m \) and the spring constant \( k \) remain unchanged when the system is taken to the Moon.

3. **Consider the Effect of Gravity**:
The time period of a spring-mass system does not depend on the acceleration due to gravity (\( g \)). It only depends on the mass and the spring constant.

4. **Conclusion**:
Since the time period does not change with gravity, the time period of the spring-mass system when taken to the Moon will remain the same as it was on Earth. Therefore, the time period on the Moon is also:
\[ T = 12 \, \text{s} \]

### Final Answer:
The time period of oscillation of the spring when taken to the Moon will be **12 seconds**.

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