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A body takes $\mathrm{n}$ times as much time to slide down a $45^{\circ}$ rough incline as it takes to slide down a smooth $45^{\circ}$ incline. The coefficient of friction between the body and the incline will be
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Verified Answer
The correct answer is:
$1-\frac{1}{n^{2}}$
The coefficient of friction,
Here,
$$
\begin{aligned}
\mu &=\tan \theta\left(1-\frac{1}{n^{2}}\right) \\
\theta &=45^{\circ}
\end{aligned}
$$
$\therefore$
$$
\mu=\tan 45^{\circ}\left(1-\frac{1}{n^{2}}\right)=1-\frac{1}{n^{2}}
$$
Here,
$$
\begin{aligned}
\mu &=\tan \theta\left(1-\frac{1}{n^{2}}\right) \\
\theta &=45^{\circ}
\end{aligned}
$$
$\therefore$
$$
\mu=\tan 45^{\circ}\left(1-\frac{1}{n^{2}}\right)=1-\frac{1}{n^{2}}
$$
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