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(A) For the beam to be in equilibrium,the net force and net torque acting on it must be zero.Three forces act on the beam: $1$. The weight $W$ of the

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(A) For the beam to be in equilibrium,the net force and net torque acting on it must be zero.Three forces act on the beam: $1$. The weight $W$ of the beam,acting vertically downwards at its center of gravity (the midpoint of the beam).$2$. The tension $T$ in the rope,acting along the rope at an angle upwards and to the left.$3$. The reaction force $R$ at the hinge $H$.Since the beam is in equilibrium,these three forces must be concurrent,meaning their lines of action must intersect at a single point.The line of action of the weight $W$ is a vertical line passing through the midpoint of the beam.The line of action of the tension $T$ is along the rope.These two lines intersect at a point above the beam. Therefore,the reaction force $R$ at the hinge must also pass through this point of intersection.Since the tension $T$ has a horizontal component to the left and a vertical component upwards,and the weight $W$ acts downwards,the reaction force $R$ must have a horizontal component to the right (to balance the horizontal component of $T$) and a vertical component upwards (to help balance the weight $W$ along with the vertical component of $T$).Thus,the reaction force $R$ must point diagonally upwards and to the right. This corresponds to the direction shown in option $A$.

$A$ uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$. The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge?

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