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 solve the question regarding the acceleration of a body rolling down an inclined plane and what it does not depend on, we will analyze each option systematically.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine which of the given options does not affect the acceleration of a body rolling down an inclined plane.

2. **Analyzing the Acceleration of a Rolling Body**:
When a body rolls down an inclined plane, its acceleration can be expressed as:
\[ a = \frac{g \sin \theta}{1 + \frac{I}{mR^2}} \]
where:
- \( g \) = acceleration due to gravity,
- \( \theta \) = angle of inclination,
- \( I \) = moment of inertia of the body,
- \( m \) = mass of the body,
- \( R \) = radius of the body.

3. **Evaluating Each Option**:
- **Option 1: Angle of inclination of the plane**:
The acceleration \( a \) depends on \( \sin \theta \). Therefore, this option is incorrect as the acceleration does depend on the angle of inclination.

- **Option 2: Length of the plane**:
The formula for acceleration does not include the length of the inclined plane. Thus, the acceleration does not depend on the length of the plane. This option is correct.

- **Option 3: Acceleration due to gravity of Earth**:
The acceleration \( a \) is directly proportional to \( g \). Hence, this option is incorrect as the acceleration does depend on the acceleration due to gravity.

- **Option 4: Radius of gyration of body**:
The radius of gyration \( k \) appears in the moment of inertia \( I \) and thus affects the acceleration. Therefore, this option is incorrect as the acceleration does depend on the radius of gyration.

4. **Conclusion**:
Based on the analysis, the only option that does not affect the acceleration of the body rolling down the inclined plane is **Option 2: Length of the plane**.

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

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