An object takes $n$ times as much time as to slide down a $45^{\circ}$ rough inclined plane as it takes to…
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
$\left(1-\frac{1}{n^2}\right)$
$\left(\frac{1}{1-n^2}\right)$
$\sqrt{1-\frac{1}{n^2}}$
$\sqrt{1+\frac{1}{n^2}}$
Solution
The coefficient of kinetic friction between the object and the rough incline
$\mu=\tan \theta\left(1-\frac{1}{n^2}\right)$
$\mu=\tan 45^{\circ}\left(1-\frac{1}{n^2}\right)$
$=1-\frac{1}{n^2}$