A simple pendulum , a physical pendulum, a torsional pendulum and a spring-mass systeam, each of same frequency are taken to the Moon. If frequencies are measured on the moon, which systeam of systeams will have it unchanged?

Options

A. spring-mass system and torisonal pendulum.
B. only spring-mass system.
C. spring-mass system and physical pendulum.
D. None of these

Answer

To solve the problem, we need to analyze the frequency of each system when taken to the Moon, where the acceleration due to gravity (g) is different from that on Earth.

### Step-by-Step Solution:

1. **Understand the systems**: We have four systems:
- Simple Pendulum
- Physical Pendulum
- Torsional Pendulum
- Spring-Mass System

2. **Frequency of Simple Pendulum**:
The frequency \( f \) of a simple pendulum is given by:
\[ f = \frac{1}{T} = \frac{1}{2\pi} \sqrt{\frac{g}{L}} \]
where \( g \) is the acceleration due to gravity and \( L \) is the length of the pendulum. Since \( g \) changes on the Moon, the frequency will change.

3. **Frequency of Physical Pendulum**:
The frequency of a physical pendulum is also dependent on \( g \):
\[ f = \frac{1}{T} = \frac{1}{2\pi} \sqrt{\frac{g}{I/mh}} \]
where \( I \) is the moment of inertia, \( m \) is the mass, and \( h \) is the distance from the pivot to the center of mass. Since \( g \) changes, the frequency will also change.

4. **Frequency of Torsional Pendulum**:
The frequency of a torsional pendulum is given by:
\[ f = \frac{1}{T} = \frac{1}{2\pi} \sqrt{\frac{k}{I}} \]
where \( k \) is the torsional constant and \( I \) is the moment of inertia. This system does not depend on \( g \), so its frequency remains unchanged on the Moon.

5. **Frequency of Spring-Mass System**:
The frequency of a spring-mass system is given by:
\[ f = \frac{1}{T} = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]
where \( k \) is the spring constant and \( m \) is the mass. This system also does not depend on \( g \), so its frequency remains unchanged on the Moon.

6. **Conclusion**:
The systems whose frequencies remain unchanged when taken to the Moon are the Torsional Pendulum and the Spring-Mass System. Therefore, the answer is that the Torsional Pendulum and Spring-Mass System will have unchanged frequencies.

### Final Answer:
The systems that will have unchanged frequencies on the Moon are the Torsional Pendulum and the Spring-Mass System.