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A given object takes n times more times to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is:

1. √(1 - 1/n²)
2. 1 - 1/n²
3. 1/(2 - n²)
4. 1/√(1 - n²)

Correct answer: 1 - 1/n²

Solution

The time taken to slide down the rough incline compared to the smooth incline is influenced by the frictional force, which reduces the acceleration. The relationship derived from the equations of motion and the forces acting on the object leads to the conclusion that the coefficient of kinetic friction is expressed as 1 - 1/n², indicating how friction affects the sliding time.

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