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Question

A plank of mass 2kg and length 1m is placed on horizontal floor. A small block of mass 1 kg is placed on top of the plank at its right extreme end. The coefficient of friction between plank and floor is 0.5 and that between plank and block is 0.2. If a horizontal force = 30Nstarts acting on the plank to the right, the time after which the block will fall off the plank is
(g=10ms2)

A
2/3
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B
1.5s
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C
0.75 s
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D
4/3
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Solution

The correct option is A 2/3
let f1 be the maximum limiting friction provided by floor and plank μmg=0.5×30=15N
similarly limiting friction provided between plank and block f2=0.2×10=2N
for plank: acceleration A=Ff1f2M=301522=6.5m/s2
for block: acceleration a=f2m=2m/s2
relative acceleration arel=4.5m/s2
so l=12arelt2
which gives t=2/3sec

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