Problem $2$: Static Equilibrium and Force Diagram

A uniform beam of mass $5$ kg and length $3$ m is supported by a hinge at one end and a rope at the other, making an angle of $30$ with the horizontal. A $10-kg$ mass is suspended $2$ m from the hinge. Find:

The tension in the rope.

The horizontal and vertical forces exerted by the hinge. What is the tension in the rope?

A$)100\mathrm{.}0$ N

B$)113\mathrm{.}5$ N

C$)120\mathrm{.}0$ N

D$)150\mathrm{.}0$ N

What is the horizontal force exerted by the hinge?

A$)90\mathrm{.}0$ N

B$)98\mathrm{.}3$ N

C$)110\mathrm{.}0$ N

D$)113\mathrm{.}5$ N

What is the vertical force exerted by the hinge?

A$)100\mathrm{.}0$ N

B$)102\mathrm{.}5$ N

C$)113\mathrm{.}5$ N

D$)120\mathrm{.}0$ N