Two unequal masses are tied together with a cord with a compressed spring in between. The cord is burned.
Which of the following energies is conserved for the system?

Options

A. (a) Kinetic energy
B. (b) Potential energy
C. (c) Mechanical energy
D. (d) None of these

Explanation

To solve the problem, we need to analyze the situation involving two unequal masses tied together with a cord and a compressed spring in between them. When the cord is burned, we need to determine which type of energy is conserved in the system.

### Step-by-Step Solution:

1. **Understand the Initial State**:
- Initially, the two masses \( m_1 \) and \( m_2 \) are at rest, meaning their kinetic energy is zero.
- The spring is compressed, which means there is potential energy stored in the spring, given by the formula \( PE = \frac{1}{2} k x^2 \), where \( k \) is the spring constant and \( x \) is the compression distance.

**Hint**: Identify the initial energies in the system before any action takes place.

2. **Action of Burning the Cord**:
- When the cord is burned, the spring will decompress, causing the two masses to move apart.
- As the spring decompresses, the potential energy stored in the spring will convert into kinetic energy of the two masses.

**Hint**: Consider the transformation of energy types when the cord is burned.

3. **Kinetic Energy After the Release**:
- After the cord is burned, the masses will have some kinetic energy as they move apart. The kinetic energy of the system can be expressed as:
\[ KE = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 \]
- Here, \( v_1 \) and \( v_2 \) are the velocities of masses \( m_1 \) and \( m_2 \) respectively.

**Hint**: Remember that kinetic energy will increase as the spring releases its stored energy.

4. **Conservation of Energy**:
- The total mechanical energy of the system is the sum of the kinetic energy and the potential energy. Initially, the total mechanical energy is purely potential energy (from the spring).
- After the cord is burned, the potential energy decreases as the spring decompresses, while the kinetic energy of the masses increases.
- Since there are no external forces acting on the system (assuming no friction or air resistance), the total mechanical energy is conserved.

**Hint**: Think about the principle of conservation of energy in a closed system.

5. **Conclusion**:
- The potential energy of the spring is converted into kinetic energy of the masses, but the total mechanical energy remains constant throughout the process.
- Therefore, the correct answer is that **mechanical energy is conserved** in the system.

### Final Answer:
The energy that is conserved for the system is **mechanical energy**.