A given object takes \( n \) times as much time to slide down a \( 45^{\circ} \) rough incline a...

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A given object takes \( n \) times as much time to slide down a \( 45^{\circ} \) rough incline as it takes to slide down a perfectly smooth \( 45^{\circ} \) incline. The coefficient of kinetic friction between the object and the incline is given by
[RPET 1999; AMU 2000; Similar AIIMS 2008]
(a) \( \left(1-\frac{1}{n^{2}}\right) \)
(b) \( \frac{1}{1-n^{2}} \)
(c) \( \sqrt{\left(1-\frac{1}{n^{2}}\right)} \)
(d) \( \sqrt{\frac{1}{1-n^{2}}} \)
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