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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 :
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Verified Answer
The correct answer is:
$1-\frac{1}{n^2}$
$1-\frac{1}{n^2}$
The coefficients of kinetic friction between the object and the incline
$\mu=\tan \theta\left(1-\frac{1}{\mathrm{n}^2}\right)$
$\Rightarrow \mu=1-\frac{1}{\mathrm{n}^2} \quad\left(\because \theta=45^{\circ}\right)$
$\mu=\tan \theta\left(1-\frac{1}{\mathrm{n}^2}\right)$
$\Rightarrow \mu=1-\frac{1}{\mathrm{n}^2} \quad\left(\because \theta=45^{\circ}\right)$
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