A body is rolling down an inclined plane. If kinetic energy of rotation is `40 %` of kinetic energy in translatory state then the body is a.

Options

A. ring
B. cylinder
C. hollow ball
D. solid ball

Explanation

To solve the problem, we need to analyze the relationship between the kinetic energy of rotation and the kinetic energy of translation for a rolling body.

### Step-by-Step Solution:

1. **Understanding Kinetic Energies**:
- The total kinetic energy (KE) of a rolling body consists of two parts: translational kinetic energy (KE_trans) and rotational kinetic energy (KE_rot).
- The translational kinetic energy is given by:
\[ KE_{\text{trans}} = \frac{1}{2} mv^2 \]
- The rotational kinetic energy is given by:
\[ KE_{\text{rot}} = \frac{1}{2} I \omega^2 \]
- Here, \(m\) is the mass of the body, \(v\) is the linear velocity, \(I\) is the moment of inertia, and \(\omega\) is the angular velocity.

2. **Given Relationship**:
- We are given that the kinetic energy of rotation is 40% of the kinetic energy of translation:
\[ KE_{\text{rot}} = 0.4 \times KE_{\text{trans}} \]

3. **Substituting the Kinetic Energies**:
- Substitute the expressions for kinetic energies into the equation:
\[ \frac{1}{2} I \omega^2 = 0.4 \times \frac{1}{2} mv^2 \]

4. **Canceling Common Terms**:
- The \(\frac{1}{2}\) cancels out from both sides:
\[ I \omega^2 = 0.4 mv^2 \]

5. **Relating Angular Velocity to Linear Velocity**:
- For a rolling object, the relationship between linear velocity \(v\) and angular velocity \(\omega\) is:
\[ \omega = \frac{v}{r} \]
- Substituting this into the equation gives:
\[ I \left(\frac{v}{r}\right)^2 = 0.4 mv^2 \]

6. **Simplifying the Equation**:
- Rearranging the equation:
\[ I \frac{v^2}{r^2} = 0.4 mv^2 \]
- Dividing both sides by \(v^2\) (assuming \(v \neq 0\)):
\[ \frac{I}{r^2} = 0.4 m \]

7. **Finding the Moment of Inertia**:
- Rearranging gives:
\[ I = 0.4 m r^2 \]
- This can be expressed as:
\[ I = \frac{2}{5} m r^2 \]

8. **Identifying the Body**:
- The moment of inertia \(I = \frac{2}{5} m r^2\) corresponds to a solid sphere.
- Therefore, the body rolling down the inclined plane is a **solid ball**.

### Conclusion:
The correct answer is **option d: solid ball**.