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Question

A small block of mass 1 kg is placed over a plank of mass 2 kg. The length of the plank is 2 m. Coefficient of friction between the block and the plank is 0.5 and the ground over which plank is placed is smooth. A constant force F=30 N is applied on the plank in horizontal direction. The time after which the block will separate from the plank is (g=10 m/s2) approximately

  1. 0.73 s
  2. 1.2 s
  3. 0.62 s
  4. 1.6 s


Solution

The correct option is A 0.73 s
Maximum frictional force between the block and the plank is
fmax=μmg=(0.5)(1)(10)=5 N
The free body diagrams of the block and the plank are shown here

Acceleration of block a1=51=5 m/s2
Acceleration of plank a2=3052=252 m/s2
Relative acceleration of plank
a=a2a1
or a=2525=7.5 m/s2
t=2sa=2×27.5=0.73 s

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