The time taken by an object to slide down $45^{\circ}$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45^{\circ}$ incline plane. The coefficient of kinetic friction between the object and the incline plane is
AIEEE 2005,JEE MAIN 2023,JEE MAIN 2018,AIIMS 2008, Difficult
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(a)$\mu = \tan \theta \left( {1 - \frac{1}{{{n^2}}}} \right)$ $ = 1 - \frac{1}{{{n^2}}}$ [As $\theta = 45^\circ $]
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