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Transcribed Image Text:### Motion of a Bead on a Frictionless Wire
#### Diagram Description:
The diagram illustrates a bead sliding without friction along a curved wire. The wire creates a path resembling a roller coaster with various peaks and valleys.
- **Point A**: The initial point where the bead begins its motion. It is at a height from which the bead descends.
- **Point B**: The lowest point in the first dip of the path.
- **Point C**: Another low point after B.
- **Point D**: A point on an upward slope.
- **Point E**: The peak following D.
- **Point F**: A point on a downward slope after E.
- **Point G**: An intermediate point before a last rise.
- **Point H**: A point on a level path after G.
The height at different points varies, affecting the speed of the bead due to gravitational potential energy being converted to kinetic energy and vice versa.
#### Physics Problem:
A bead slides without friction on a curved wire as shown in the figure above. How do the speeds at points B, D, F, and H compare?
#### Answer Options:
A. \( v_B > v_D > v_F = v_H \)
B. \( v_B = v_D = v_F > v_H \)
C. \( v_B > v_D > v_F = v_H \)
D. \( v_B = v_F = v_D > v_H \)
E. \( v_B = v_D = v_F = v_H \)
This illustration is used to understand energy conservation in a mechanical system where all potential energy differences lead to changes in kinetic energy, impacting the speed of the bead at various points.
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