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  4. Starting from rest, the time taken by a body sliding down on a rough inclined plane at 45° 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

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Q. 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

BITSATBITSAT 2008

Solution:

$\mu=\tan \theta 1-\frac{1}{n^{2}}$
Here, $\theta=45^{\circ}$ and $n=2$
$\therefore \mu=\tan 45^{\circ} 1-\frac{1}{2^{2}}$
$=1-\frac{1}{4}=\frac{3}{4}=0.75$