Moment of inertia of a sphere of mass M and radius R is I. Keeping M constant if a graph is plotted between I and R, then its form would be

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Answer

To determine the relationship between the moment of inertia (I) of a sphere and its radius (R), we start with the formula for the moment of inertia of a solid sphere about an axis through its center:

\[ I = \frac{2}{5} M R^2 \]

Where:
- \( I \) is the moment of inertia,
- \( M \) is the mass of the sphere (which is kept constant),
- \( R \) is the radius of the sphere.

### Step-by-Step Solution:

1. **Identify the relationship**: From the formula \( I = \frac{2}{5} M R^2 \), we can see that the moment of inertia \( I \) is proportional to the square of the radius \( R \) when mass \( M \) is constant.

2. **Express the proportionality**: Since \( I \) is proportional to \( R^2 \), we can write this relationship as:
\[ I \propto R^2 \]

3. **Graphical representation**: When we plot \( I \) on the y-axis and \( R \) on the x-axis, the equation \( I = k R^2 \) (where \( k = \frac{2}{5} M \)) represents a parabolic curve opening upwards.

4. **Conclusion about the graph**: The graph of \( I \) versus \( R \) will be a parabola. Specifically, it will be symmetric about the y-axis, indicating that as \( R \) increases, \( I \) increases quadratically.

### Final Answer:
The graph between the moment of inertia \( I \) and the radius \( R \) of a sphere, keeping mass \( M \) constant, will be a parabola opening upwards.