The figure below shows four different cases involving a uniform rod of length L and mass M, which is subjected to two forces of equal magnitude. The rod is free to rotate about an axis that either passes through one end of the rod, as in (a) and (b), or passes through the middle of the rod, as in (c) and (d). The axis is marked by the red and black circle, and is perpendicular to the page in each case. This is an overhead view, and we can neglect any effect of the force of gravity acting on the rod. Rank these four situations based on the magnitude of the net torque about the axis, from largest to smallest. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.) (a) F (b) F (c) F (d) F F F F |F

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The figure illustrates four scenarios involving a uniform rod of length \( L \) and mass \( M \), subject to two forces of equal magnitude. The rod can rotate about an axis located either at one end of the rod, as depicted in cases (a) and (b), or through the middle of the rod, as shown in cases (c) and (d). The axis is denoted by the red and black circle and is perpendicular to the page in each situation. 

This is an overhead view, and the influence of gravity on the rod can be disregarded. The task is to rank these four situations based on the magnitude of the net torque about the axis, from largest to smallest. Only ">" or "=" symbols should be used without parentheses around the letters or symbols.

**Descriptions of Diagrams:**

1. **Diagram (a):**
   - The rod is horizontal with an axis at the left end.
   - One force \( F \) acts upward at the left end, coincident with the axis.
   - Another force \( F \) acts downward on the right end of the rod.

2. **Diagram (b):**
   - The rod is horizontal with an axis at the right end.
   - One force \( F \) acts downward at the right end, coincident with the axis.
   - Another force \( F \) acts upward on the left end of the rod.

3. **Diagram (c):**
   - The rod's axis is in the middle.
   - Two forces \( F \) act in opposite directions: upward on the left half and downward on the right half, symmetrically about the axis.

4. **Diagram (d):**
   - Similar to diagram (c), with the axis in the middle.
   - The forces \( F \) still act in opposite directions: upward on the left half and downward on the right half, symmetrically about the axis.
Transcribed Image Text:The figure illustrates four scenarios involving a uniform rod of length \( L \) and mass \( M \), subject to two forces of equal magnitude. The rod can rotate about an axis located either at one end of the rod, as depicted in cases (a) and (b), or through the middle of the rod, as shown in cases (c) and (d). The axis is denoted by the red and black circle and is perpendicular to the page in each situation. This is an overhead view, and the influence of gravity on the rod can be disregarded. The task is to rank these four situations based on the magnitude of the net torque about the axis, from largest to smallest. Only ">" or "=" symbols should be used without parentheses around the letters or symbols. **Descriptions of Diagrams:** 1. **Diagram (a):** - The rod is horizontal with an axis at the left end. - One force \( F \) acts upward at the left end, coincident with the axis. - Another force \( F \) acts downward on the right end of the rod. 2. **Diagram (b):** - The rod is horizontal with an axis at the right end. - One force \( F \) acts downward at the right end, coincident with the axis. - Another force \( F \) acts upward on the left end of the rod. 3. **Diagram (c):** - The rod's axis is in the middle. - Two forces \( F \) act in opposite directions: upward on the left half and downward on the right half, symmetrically about the axis. 4. **Diagram (d):** - Similar to diagram (c), with the axis in the middle. - The forces \( F \) still act in opposite directions: upward on the left half and downward on the right half, symmetrically about the axis.
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