The relation between angular momentum J of a body and rotational kinetic energy is given by `J=sqrt(2EI)`. The graph between J and `sqrt(E)` will be:

Options

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Answer

To solve the problem, we need to analyze the relationship between angular momentum \( J \) and rotational kinetic energy \( E \) as given by the equation:

\[ J = \sqrt{2EI} \]

### Step-by-Step Solution:

1. **Identify the Variables**:
- We have \( J \) as the angular momentum.
- We have \( E \) as the rotational kinetic energy.
- We need to establish the relationship between \( J \) and \( \sqrt{E} \).

2. **Rearranging the Equation**:
- From the equation \( J = \sqrt{2EI} \), we can express \( J \) in terms of \( \sqrt{E} \):
\[ J = \sqrt{2I} \cdot \sqrt{E} \]
- This shows that \( J \) is directly proportional to \( \sqrt{E} \).

3. **Understanding the Proportionality**:
- Since \( J \) is directly proportional to \( \sqrt{E} \), we can write:
\[ J = k \cdot \sqrt{E} \]
where \( k = \sqrt{2I} \) is a constant.

4. **Graphical Representation**:
- In a graph where \( J \) is plotted on the Y-axis and \( \sqrt{E} \) is plotted on the X-axis, the relationship \( J = k \cdot \sqrt{E} \) indicates that the graph will be a straight line.
- The slope of the line is positive since \( k \) is a positive constant.

5. **Intercept Analysis**:
- If \( \sqrt{E} = 0 \), then \( J \) will also be \( 0 \). This means the graph passes through the origin (0,0).

6. **Conclusion**:
- Therefore, the graph between \( J \) and \( \sqrt{E} \) is a straight line that passes through the origin and has a positive slope.

### Final Answer:
The graph between \( J \) and \( \sqrt{E} \) will be a straight line passing through the origin.

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