The `P.E.` of an oscillation particle at rest position is `10J` and its average `K.E.` is `5J`. The total energy of particle at any instant will be-

Options

A. `10 J`
B. `20 J`
C. `25 J`
D. `5 J`

Explanation

To solve the problem, we need to determine the total energy of an oscillating particle given its potential energy (P.E.) at the rest position and its average kinetic energy (K.E.).

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The potential energy (P.E.) of the particle at the rest position is given as \(10 \, \text{J}\).
- The average kinetic energy (K.E.) of the particle is given as \(5 \, \text{J}\).

2. **Identify Energy Conservation**:
- In simple harmonic motion, the total mechanical energy (E) of the system is conserved. This means that the total energy is the sum of the potential energy and kinetic energy at any point in time.
- Mathematically, this can be expressed as:
\[ E = \text{P.E.} + \text{K.E.} \]

3. **Calculate Total Energy**:
- At the rest position, the potential energy is at its maximum, and the kinetic energy is zero. Therefore, the total energy at this position is:
\[ E = \text{P.E.} + 0 = 10 \, \text{J} \]

4. **Determine Total Energy at Any Instant**:
- The total energy of the particle remains constant throughout its motion. Therefore, the total energy at any instant will also be \(10 \, \text{J}\).

5. **Conclusion**:
- The total energy of the particle at any instant is \(10 \, \text{J}\).

### Final Answer:
The total energy of the particle at any instant will be \(10 \, \text{J}\).

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