Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the…

Starting from rest, the time taken by a body sliding down on a rough inclined plane at $45^{\circ}$ with the horizontal is, twice the time taken to travel on a smooth plane of same inclination and same distance. Then the coefficient of kinetic friction is
  1. $0.25$
  2. $0.33$
  3. $0.50$
  4. $0.75$

Solution

$ \mu=\tan \theta\left[1-\frac{1}{n^2}\right] $ Here, $\quad \theta=45^{\circ}$ and $n=2$ $\begin{aligned} \therefore \quad \mu & =\tan 45^{\circ}\left[1-\frac{1}{2^2}\right] \\ & =1-\frac{1}{4}=\frac{3}{4}=0.75\end{aligned}$

Asked in: AP EAMCET 2008

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