AP EAMCET · PHYSICS · Laws of Motion
An object takes \(n\) times as much time as to slide down a \(45^{\circ}\) rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by
- A \(\left(1-\frac{1}{n^2}\right)\)
- B \(\left(\frac{1}{1-n^2}\right)\)
- C \(\sqrt{1-\frac{1}{n^2}}\)
- D \(\sqrt{1+\frac{1}{n^2}}\)
Answer & Solution
Correct Answer
(A) \(\left(1-\frac{1}{n^2}\right)\)
Step-by-step Solution
Detailed explanation
The coefficient of kinetic friction between the object and the rough incline \(\mu=\tan \theta\left(1-\frac{1}{n^2}\right)\) \(\mu=\tan 45^{\circ}\left(1-\frac{1}{n^2}\right)\) \(=1-\frac{1}{n^2}\)
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