A system consists of n identical particles each of mass m. The total number of interaction potential energy terms possible are `(n(n-1))/x`. Find value of x.

Explanation

To solve the problem, we need to find the value of \( x \) in the expression for the total number of interaction potential energy terms possible among \( n \) identical particles, which is given as:

\[ \frac{n(n-1)}{x} \]

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have \( n \) identical particles, each with mass \( m \).
- We need to calculate the total number of interaction potential energy terms between these particles.

2. **Identifying Interactions**:
- Each pair of particles can interact with each other. For \( n \) particles, the number of ways to choose 2 particles from \( n \) is given by the combination formula \( C(n, 2) \).
- The formula for combinations is:
\[ C(n, 2) = \frac{n!}{2!(n-2)!} = \frac{n(n-1)}{2} \]

3. **Calculating Total Interactions**:
- The total number of interaction potential energy terms is therefore:
\[ \text{Total Interactions} = \frac{n(n-1)}{2} \]

4. **Setting Up the Equation**:
- According to the problem, this total number of interactions is also given by:
\[ \frac{n(n-1)}{x} \]
- We can set the two expressions equal to each other:
\[ \frac{n(n-1)}{2} = \frac{n(n-1)}{x} \]

5. **Solving for \( x \)**:
- Since \( n(n-1) \) is common on both sides (and assuming \( n \neq 0 \) and \( n \neq 1 \)), we can cancel it out:
\[ \frac{1}{2} = \frac{1}{x} \]
- Cross-multiplying gives:
\[ x = 2 \]

### Final Answer:
The value of \( x \) is \( 2 \).

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