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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

  1. 0.6 and 0.6
  2. 0.4 and 0.3
  3. 0.6 and 0.5
  4. 0.5 and 0.6


Solution

The correct option is C 0.6 and 0.5
Static friction
μs=tanθ [θ-At which it starts to slide]
μs=tan30=13=0.6
Now as the body slips down, acceleration =gsinθμkgcosθ
=gsin30μkgcos30
s=ut+12at2
4=0+12[g(12)μ×g32]t2
4=12[g2μkg32]16
12=12(g)[13μk]
13μk=110
13μk=0.1
μk=0.93=0.52

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