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To determine which object has the greater total kinetic energy, we need to analyze both the translational and rotational kinetic energies of the two pucks.

**Given:**
1. Two pucks (red and blue) slide on ice with little friction.
2. A string is pulled with a constant force \( F \) on both pucks.
3. The string is wound around the outer edge of puck 1 (red) and attached to the center of puck 2 (blue).
4. Both pucks start from rest.

### Analysis:
1. **Puck 1 (Red) - String wound around the outer edge:**
   - The force \( F \) causes both translational and rotational motion.
   - Translational kinetic energy: \( KE_{\text{trans,1}} = \frac{1}{2} m v_1^2 \)
   - Rotational kinetic energy: \( KE_{\text{rot,1}} = \frac{1}{2} I \omega_1^2 \)
     - Where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.
     - For a disk, \( I = \frac{1}{2} m r^2 \)
     - \( \omega_1 = \frac{v_1}{r} \)

2. **Puck 2 (Blue) - String attached to the center:**
   - The force \( F \) only causes translational motion.
   - Translational kinetic energy: \( KE_{\text{trans,2}} = \frac{1}{2} m v_2^2 \)

### Total Kinetic Energy:
For Puck 1 (Red):
\[ KE_{\text{total,1}} = \frac{1}{2} m v_1^2 + \frac{1}{2} \left(\frac{1}{2} m r^2 \right) \left( \frac{v_1}{r} \right)^2 \]
\[ KE_{\text{total,1}} = \frac{1}{2} m v_1^2 + \frac{1}{4} m v_1^2 \]
\[ KE_{\text{total,1}} = \frac{3}{4} m v_1^2 \]

For Puck 2 (Blue):
\[ KE_{\text{total,2}} = \frac{1}{2} m v_2^2 \]

### Comparing the Kinetic Energies:
The key point here is that both pucks are subjected to the same force \( F \), but the red puck (Puck 1) also has rotational kinetic energy due to the string being wound around its edge. As a result, the red puck will have a greater total kinetic energy than the blue puck (Puck 2), since the blue puck only has translational kinetic energy.

Thus, the answer is:

**C. Top object (red)**

Would you like more details or have any questions about the explanation?

Here are five questions you might consider next:
1. How do you calculate the moment of inertia for different shapes?
2. What is the difference between translational and rotational kinetic energy?
3. How does force relate to work and energy?
4. What are the effects of friction on kinetic energy?
5. How do you calculate angular velocity and its relation to linear velocity?

**Tip:** Remember that kinetic energy can come in both translational and rotational forms, especially when dealing with objects that can spin or rotate.

Explore the comparison of kinetic energies in translational and rotational motion scenarios. Analyze the effects of forces on pucks sliding on ice with low friction, and understand how kinetic energy is distributed between translational and rotational components. Suitable for advanced high school students studying mechanics and rotational dynamics.

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