The acceleration of a body rolling down on an inclined plane does not depend upon

Options

A. Angle of inclination of the plane
B. Length of plane
C. Acceleration due to gravity of earth
D. Radius of gyration of body

Answer

To determine what the acceleration of a body rolling down an inclined plane does not depend upon, we can analyze the formula for the acceleration of a rolling object.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- We have a body (which could be a solid cylinder, hollow cylinder, disc, etc.) rolling down an inclined plane at an angle θ.

2. **Acceleration Formula**:
- The acceleration \( a \) of a body rolling down an incline can be expressed with the formula:
\[ a = \frac{g \sin(\theta)}{1 + \frac{I}{m r^2}} \]
- Where:
- \( g \) = acceleration due to gravity,
- \( I \) = moment of inertia of the body,
- \( m \) = mass of the body,
- \( r \) = radius of the body.

3. **Analyzing Dependencies**:
- From the formula, we can see that:
- The acceleration \( a \) is directly proportional to \( g \) (it depends on gravity).
- The acceleration \( a \) is also directly proportional to \( \sin(\theta) \) (it depends on the angle of inclination).
- The term \( \frac{I}{m r^2} \) indicates that the acceleration depends on the moment of inertia and the radius of the object.

4. **Identifying What It Does Not Depend On**:
- Now, we need to identify which factor does not appear in the formula:
- **Length of the incline**: The length of the incline does not appear in the formula, meaning the acceleration does not depend on the length of the incline.
- **Angle of Inclination**: It does depend on the angle of inclination as seen from the \( \sin(\theta) \) term.
- **Acceleration due to Gravity**: It does depend on \( g \).
- **Radius of Gyration**: Since the moment of inertia is related to the radius of gyration, it does depend on the radius of gyration.

5. **Conclusion**:
- Therefore, the acceleration of a body rolling down an inclined plane does not depend on the **length of the incline**.

### Final Answer:
The acceleration of a body rolling down an inclined plane does not depend upon the **length of the incline**.