Question

Assuming frictionless contacts, determine the magnitude of external horizontal force P applied at the lower end for equilibrium of the rod. The rod is uniform and its mass is 'm'.

Answer 1

$N=P$

Torque balance is;

$mg\left(\frac{l}{2}\right)\cos \theta =Nl\sin \theta$

$N=\left(\frac{mg}{2}\right)\cot \theta$

$P=\left(\frac{mg}{2}\right)\cot \theta$