A marble is allowed to roll down an inclined plane from a fixed height. At the foot of the inclined plane, it moves on a horizontal surface (a) covered with silk cloth (b) covered with a layer of sand and (c) covered with a glass sheet. On which surface will the marble move the shortest distance. Give reason for your answer.

Options

A. covered with silk cloth
B. covered with a layer of sand
C. covered with a glass sheet
D. none of these

Explanation

To determine on which surface the marble will move the shortest distance after rolling down an inclined plane, we need to analyze the effects of friction on each surface.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- A marble rolls down an inclined plane and reaches the bottom where it encounters three different surfaces: silk cloth, sand, and a glass sheet.

2. **Identifying the Surfaces**:
- **Silk Cloth**: This surface is smooth and has low friction.
- **Sand**: This surface is rough and has high friction.
- **Glass Sheet**: This surface is also smooth but typically has slightly higher friction than silk.

3. **Effect of Friction**:
- Friction opposes the motion of the marble. The greater the friction, the shorter the distance the marble will travel.
- The rougher the surface, the more friction it produces.

4. **Comparing the Surfaces**:
- On the **silk cloth**, the marble will experience minimal friction, allowing it to roll a longer distance.
- On the **glass sheet**, the friction is low but higher than that of silk, so the marble will roll a shorter distance than on silk but longer than on sand.
- On the **sand**, the roughness creates significant friction, which will greatly oppose the marble's motion, causing it to stop much sooner.

5. **Conclusion**:
- Since sand has the highest friction among the three surfaces, the marble will travel the shortest distance on the sand. Therefore, the answer is that the marble will move the shortest distance on the surface covered with sand.

### Final Answer:
The marble will move the shortest distance on the surface covered with sand due to the high friction that opposes its motion.

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