Which of the following will change the time period as they are taken to moon?

Options

A. A simple pendulum
B. A Physical pendulum
C. A torsional pendulum
D. A spring mass system

Answer

To determine which of the given systems will change the time period when taken to the moon, we need to analyze the time period formulas for each system and see if they depend on the acceleration due to gravity (g).

### Step-by-Step Solution:

1. **Understanding the Acceleration Due to Gravity**:
- On Earth, the acceleration due to gravity (g) is approximately 9.8 m/s².
- On the Moon, the acceleration due to gravity is about \( \frac{g}{6} \) or approximately 1.63 m/s².

2. **Analyzing Each Option**:
- **Option 1: Simple Pendulum**:
- The time period (T) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Since this formula includes g, the time period will change when taken to the moon (because g changes).

- **Option 2: Physical Pendulum**:
- The time period (T) of a physical pendulum is given by:
\[ T = 2\pi \sqrt{\frac{I}{mgl}} \]
- This formula also includes g, so the time period will change when taken to the moon.

- **Option 3: Torsional Pendulum**:
- The time period (T) of a torsional pendulum is given by:
\[ T = 2\pi \sqrt{\frac{I}{k}} \]
- This formula does not include g, so the time period will not change when taken to the moon.

- **Option 4: Spring Mass System**:
- The time period (T) of a spring mass system is given by:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
- This formula also does not include g, so the time period will not change when taken to the moon.

3. **Conclusion**:
- The systems whose time periods will change when taken to the moon are:
- **Simple Pendulum (Option 1)**
- **Physical Pendulum (Option 2)**
- The Torsional Pendulum (Option 3) and Spring Mass System (Option 4) will not change their time periods.

### Final Answer:
- The time period will change for:
- **Option 1: Simple Pendulum**
- **Option 2: Physical Pendulum**