Question

# 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 coeffficient of static and kinetic friction between the box and the plank will respectively be

A
0.4 and 0.3
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B
0.6 and 0.6
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C
0.6 and 0.5
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D
0.5 and 0.6
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Solution

## The correct option is A 0.6 and 0.5Static friction μs=tanθ [θ-At which it starts to slide] μs=tan30∘=1√3=0.6 Now as the body slips down, acceleration =gsinθ−μkgcosθ =gsin30∘−μkgcos30∘ s=ut+12at2 4=0+12[g(12)−μ×g√32]t2 4=12[g2−μkg√32]16 12=12(g)[1−√3μk] 1−√3μk=110 1−√3μk=0.1 μk=0.9√3=0.52

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