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:

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Answer

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

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

### Step 1: Rearranging the Equation
We can express the equation in a more useful form for graphing. Squaring both sides gives:

\[ J^2 = 2EI \]

### Step 2: Expressing Energy in Terms of J
From the equation \( J^2 = 2EI \), we can express \( E \) in terms of \( J \):

\[ E = \frac{J^2}{2I} \]

### Step 3: Identifying the Variables
In this equation:
- \( J \) is on the y-axis (dependent variable).
- \( E \) is on the x-axis (independent variable).
- The constant \( \frac{1}{2I} \) acts as the slope of the line when we plot \( E \) against \( J^2 \).

### Step 4: Analyzing the Graph
The equation \( E = \frac{1}{2I} J^2 \) represents a quadratic relationship between \( E \) and \( J \). However, since we want to plot \( J \) against \( \sqrt{E} \), we need to express \( J \) in terms of \( \sqrt{E} \).

### Step 5: Expressing J in Terms of sqrt(E)
Taking the square root of both sides of the rearranged equation gives:

\[ J = \sqrt{2I} \cdot \sqrt{E} \]

### Step 6: Graph Characteristics
This equation \( J = \sqrt{2I} \cdot \sqrt{E} \) indicates that:
- The graph will be a straight line.
- It passes through the origin because when \( E = 0 \), \( J \) will also be \( 0 \).
- The slope of the line is \( \sqrt{2I} \).

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