A thin rod of mass M and length is connected to a wall by a

A thin rod of mass M and length ` is connected to a wall by a hinge. The rod is horizontal, and it is held stationary by a massless cable running from its free end to the wall. The cable makes an angle ? with the horizontal.

(a) What is the tension in the cable?

(b) What are the components of the force of the rod on the hinge?

Solution

A

Calculate torques about the hinge.
Torque of weight = mg * L/2 cos(phi)

B

Net horizontal force = 0.
Therefore horizontal component of foce by the hinge = T

Net vertical force = 0
Therefore vertical component of force by the hinge = mg