The work done by a conservative force between two points is always positive and independent of the path taken. It is not dependent on time and can be completely recoverable depending on the nature of the force and the system involved. The correct answer is option c. Always positive and always independent of the path.
The work done by a conservative force between two points depends on the nature of the force and the path taken. A conservative force is one for which the work done depends only on the initial and final positions, not on the path taken.
Let's analyze the given options:
a. Always dependent upon the time.
- This option is incorrect. The work done by a conservative force is not dependent on time but rather on the initial and final positions.
b. Never completely recoverable.
- This option is incorrect. The recoverability of work depends on the nature of the force and the system involved. Some conservative forces, such as gravitational and elastic forces, can completely recover the work done.
c. Always positive and always independent of the path.
- This option is correct. A conservative force always does positive work and is path-independent. This means that the work done by a conservative force is the same regardless of the path taken between two points, as long as the initial and final positions remain the same.
d. Zero.
- This option is incorrect. The work done by a conservative force is not always zero. It is only zero in situations where the initial and final positions are the same, indicating that no net work is done.