Show all work, clearly indicate answer, and use correct units for full credit.

A $4\mathrm{.}00$m long, $50\mathrm{.}0$kg bar is attached to a wall by a hinge and held up by rope attached at a $25$ angle $1\mathrm{.}00$ m from the far end of the bar.

a$)$ What is the tension of the rope?

b$)$ What is the magnitude and direction of the force on the hinge?

c$)$ An object is place on the far end of the bar and the tension doubles. What is the mass of this object?