A body is attached to a spring whose other end is fixed. If the spring is elongated by x, its potential energy is `U=5x^2`, where x is in metre and U is in joule. U-x graph is

Options

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Explanation

To solve the problem of finding the U-x graph for the given potential energy equation \( U = 5x^2 \), we can follow these steps:

### Step 1: Understand the Given Equation
The potential energy \( U \) is given by the equation:
\[ U = 5x^2 \]
where \( U \) is in joules and \( x \) is in meters.

### Step 2: Identify the Nature of the Equation
The equation \( U = 5x^2 \) is a quadratic equation in terms of \( x \). Since it is in the form \( U = ax^2 \) (where \( a = 5 \)), we can conclude that the graph will be a parabola.

### Step 3: Determine the Orientation of the Parabola
Since the coefficient of \( x^2 \) (which is 5) is positive, the parabola opens upwards. This means that as \( x \) increases or decreases from zero, the potential energy \( U \) will increase.

### Step 4: Find the Value of Potential Energy at \( x = 0 \)
To find the y-intercept of the graph, we can substitute \( x = 0 \) into the equation:
\[ U = 5(0)^2 = 0 \]
This indicates that when \( x = 0 \), \( U = 0 \). Therefore, the graph will pass through the origin (0,0).

### Step 5: Sketch the Graph
Based on the above information, we can sketch the graph:
- The graph is a parabola that opens upwards.
- It passes through the origin (0,0).

### Step 6: Analyze the Options
If presented with multiple-choice options, we would look for a graph that:
- Is a parabola opening upwards.
- Passes through the origin (0,0).

### Conclusion
Based on the analysis, the correct U-x graph is the one that is a parabola opening upwards and passes through the origin.

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