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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
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The correct answer is:
$\left(1-\frac{1}{n^2}\right)$
The coefficient of kinetic friction between the object and the rough incline
$\mu=\tan \theta\left(1-\frac{1}{n^2}\right)$
$\mu=\tan 45^{\circ}\left(1-\frac{1}{n^2}\right)$
$=1-\frac{1}{n^2}$
$\mu=\tan \theta\left(1-\frac{1}{n^2}\right)$
$\mu=\tan 45^{\circ}\left(1-\frac{1}{n^2}\right)$
$=1-\frac{1}{n^2}$
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