First slide

Friction on inclined plane of angle more than angle of repose

Question

Starting from rest, a body slides down a 45⁰ inclined plane in twice the time, it takes to slide down the
same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is

Moderate

A

0.2
B

0.25
C

0.75
D

0.5

Solution

For smooth surface, $a_{1} = g \sin 45 °, t_{1} = t$
For rough surface, $a_{2} = g \sin 45 ° - μ g \cos 45 °, t_{2} = 2 t$
$∴ s = \frac{1}{2} a_{1} t_{1}^{2} = \frac{1}{2} a_{2} t_{2}^{2}$ $(∵ s = \frac{1}{2} a t^{2})$
$\Rightarrow (g \sin 45 °) t^{2} = (g \sin 45 ° - μ g \cos 45 °) (2 t)^{2}$
$\Rightarrow 1 = (1 - μ) 4 \Rightarrow μ = \frac{3}{4} = 0.75$

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