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A body takes $1 \frac{1}{3}$ times as much time to slide down a rough inclined plane as it takes to slide down an identical but smooth inclined plane. If the angle of inclination is 45⁰, the coefficient of friction is

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$\frac{1}{16}$

$\frac{3}{16}$

$\frac{7}{16}$

$\frac{5}{16}$

answer is D.

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Detailed Solution

On smooth inclined plane acceleration $a_{1} = g \sin θ$ .on rough inclined plane, acceleration $a_{2} = g (sinθ - μ_{k} cosθ)$ .

If S be the length of inclined path, $t_{1} = \sqrt{\frac{2 s}{a_{1}}}$ and $t_{2} = \sqrt{\frac{2 s}{a_{2}}}$

Now $t_{2} = 1 \frac{1}{3} t_{1}$

On solving we get $μ = \frac{7}{16}$

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