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Question

A stationary uniform rod of mass m=1 kg and length l=2 m leans against a smooth vertical wall making an angle θ=45o with rough horizontal floor. Find the frictional force that is exerted by the floor on the rod.
 

  1. 15 N
  2. 5 N
  3. 10 N
  4. 20 N


Solution

The correct option is B 5 N
As the rod is stationary so the linear acceleration and angular acceleration of rod is zero. 
i.e., acom=0; α=0
N2=fN1=mg}acom=0


Torque about any point of the rod should also be zero 
α=0
τA=0mgcosθl2+f lsinθ=N1.lcosθ
N1cos θ=fsinθ+mgcosθ2
f=mgcosθ2sinθ=mgcotθ2
f=1×10×cot45o2
f=102=5 N
So, option (a) is correct. 

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