A given object takes $n$ times more time to slide down a $45^{\circ}$ rough inclined plane as it takes to…
A given object takes $n$ times more time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is :
$\sqrt{1-\frac{1}{n^2}}$
$1-\frac{1}{n^2}$
$\frac{1}{2-n^2}$
$\sqrt{\frac{1}{1-n^2}}$
Solution
The coefficients of kinetic friction between the object and the incline
$\mu=\tan \theta\left(1-\frac{1}{\mathrm{n}^2}\right)$
$\Rightarrow \mu=1-\frac{1}{\mathrm{n}^2} \quad\left(\because \theta=45^{\circ}\right)$