A solid sphere, disc and hollow sphere are placed at the top of an inclined plane. Surface is sufficiently rough to provide pure rolling. All the objects are released from a state of rest

Options

A. Solid sphere reaches the bottom first
B. Disc reaches the bottom first
C. Hollow sphere reaches the bottom first
D. All three objects reach the bottom simultaneously.

Explanation

To determine which object (solid sphere, disc, or hollow sphere) will reach the bottom of an inclined plane first when released from rest, we can analyze the motion of each object using the principles of rotational motion and the concept of pure rolling.

### Step-by-Step Solution:

1. **Understanding the Forces and Motion**:
- When an object rolls down an incline, it experiences a gravitational force acting downwards, which can be resolved into two components: one parallel to the incline (mg sin θ) and one perpendicular to the incline (mg cos θ).
- The frictional force is sufficient to ensure pure rolling, meaning the object rolls without slipping.

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