A plank with a box on it at one end is gradually raised about the… | NEET 2015 (AIPMT)

Q26NEET 2015 · AIPMTMedium

Friction on an Incline

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s.

The coefficients of static and kinetic friction between the box and the plank will be, respectively

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Answer: (d)

Slipping starts at $30^\circ$ : $\mu_s = \tan 30^\circ = 0.577 \approx 0.6$ .
From rest: $4 = \tfrac{1}{2}a(4)^2 \Rightarrow a = 0.5\text{ m/s}^2$ .
$a = g(\sin 30^\circ - \mu_k\cos 30^\circ) \Rightarrow 0.5 = 10(0.5 - 0.866\mu_k)$
$\mu_k = \dfrac{0.45}{0.866} \approx 0.5$
So the answer is (d) 0.6 and 0.5.

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Friction on an Incline question from NEET 2015 (AIPMT)

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