A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionsless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling) :

Options

A. solid sphere
B. hollow sphere
C. ring
D. all have the same acceleration

Explanation

To solve the problem of determining which object (a solid sphere, a hollow sphere, or a ring) has the maximum acceleration down a frictionless inclined plane when they slide without rolling, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Forces Acting on the Objects**:
- When the objects are released on a frictionless inclined plane, the only force acting on them is the component of gravitational force parallel to the incline. This force is given by \( F = mg \sin \theta \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( \theta \) is the angle of the incline.

2. **Apply Newton's Second Law**:
- According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration \( (F = ma) \).
- For each object, the net force acting down the incline is \( mg \sin \theta \). Therefore, we can write:
\[ mg \sin \theta = ma \]
- Simplifying this gives us:
\[ a = g \sin \theta \]

3. **Analyze the Acceleration for Each Object**:
- Since the expression for acceleration \( a = g \sin \theta \) does not depend on the mass or the shape of the object, it indicates that all objects will experience the same acceleration down the incline.
- This means that the solid sphere, hollow sphere, and ring will all have the same acceleration when sliding down the frictionless incline.

4. **Conclusion**:
- Therefore, the maximum acceleration down the plane is the same for all three objects. The correct answer is that they all have the same maximum acceleration.

### Final Answer:
The maximum acceleration down the plane is the same for the solid sphere, hollow sphere, and ring.