A solid sphere is thrown up a rough incline. The sphere rolls up without slipping and eventually comes down rolling without slipping. The direction of friction during upward and downward motion respectively is :-

Options

A. Downward, upward
B. Upward, downward
C. Downward, downward
D. Upward, upward

Answer

To solve the problem of determining the direction of friction when a solid sphere rolls up and down a rough incline, we can break down the analysis into clear steps.

### Step-by-Step Solution:

1. **Understanding the Motion**:
- When the solid sphere is thrown up the incline, it experiences a force due to gravity acting downwards. This force tends to make the sphere slide back down the incline.

2. **Direction of Friction During Upward Motion**:
- As the sphere rolls up the incline, the frictional force acts to oppose the relative motion between the sphere and the incline. Since the sphere is moving upwards but gravity pulls it downwards, the friction must act upwards to prevent slipping.
- Therefore, during the upward motion, the direction of friction is **upward**.

3. **Understanding the Motion During Downward Motion**:
- When the sphere reaches its highest point and starts rolling back down, it again experiences the force of gravity acting downwards.
- As the sphere rolls down, it tends to slide down the incline due to gravity. The frictional force will act in the opposite direction to the motion of the sphere to prevent slipping.
- Since the sphere is rolling downwards, the frictional force will act **upward** to oppose this motion.

4. **Conclusion**:
- Therefore, the direction of friction during the upward motion is **upward**, and during the downward motion, it is also **upward**.

### Final Answer:
The direction of friction during upward and downward motion respectively is **upward** and **upward**.