Question

Assuming frictionless contacts, determine the magnitude of external horizontal force $P$ applied at the lower end for equilibrium of the rod as shown in figure. The rod is uniform and its mass is ${}^{\prime }{m}^{\prime }$.

Answer 1

Taking moment about the wall.

$\Rightarrow -mg\cos \theta \frac{L}{2}+P\sin \theta L=0$

$\Rightarrow P=\frac{mg\cot \theta }{2}$

Hence, solved.