In the above problem, direction of friction force is

Options

A. towards left if `F_(1)` is applied
B. towards left if `F_(2)` is applied
C. towards right if `F_(3)` is applied
D. may be right or left or friction may be zero if `F_(4)` is applied

Answer

To determine the direction of the friction force in the given problem, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Identify the Forces Acting on the Spool:**
- We have several forces acting on the spool: F1, F2, F3, and F4. Each of these forces can cause the spool to move and rotate in different directions.

2. **Analyze the Motion Due to Applied Forces:**
- When F1 is applied to the left, the spool will move left and rotate clockwise. The friction force will act to oppose this motion, which means it will act to the right.
- When F2 is applied to the right, the spool will move right and rotate anticlockwise. The friction force will act to oppose this motion, which means it will act to the left.

3. **Consider the Effects of F3:**
- If F3 is applied, the direction of the motion and rotation will depend on the magnitude of F3. If it is strong enough to move the spool to the left, it will rotate anticlockwise, and the friction force will act to the right to oppose this motion.

4. **Evaluate the Case for F4:**
- F4 can have varying effects depending on its direction and magnitude. If F4 causes the spool to move left and rotate anticlockwise, the friction will act to the right. If F4 is not strong enough to cause movement, friction may be zero.

5. **Conclusion on the Direction of Friction:**
- Based on the analysis, the direction of the friction force depends on the applied forces:
- For F1: Friction acts to the right.
- For F2: Friction acts to the left.
- For F3: Friction can act to the right or left depending on the net effect.
- For F4: Friction may be zero or act to the left or right depending on the conditions.

### Final Answer:
The direction of the friction force can be:
- Rightward when F1 is applied.
- Leftward when F2 is applied.
- Indeterminate for F3 depending on its strength.
- Zero, leftward, or rightward for F4 depending on its effect.