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.   15 N5 N10 N20 N

Solution

## The correct option is B 5 NAs 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=0⇒mgcosθl2+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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