A uniform rigid rod of weight W is hinged to the ground at its lower end. It is held in equilibrium at an angle with the horizontal by a horizontal string attached to its upper end. The tension in the horizontal string is :

Step-by-step solution

Let the length of the rod be L . The rod is in rotational equilibrium. Taking torque about the hinge at the ground, the forces producing torque are the weight of the rod W and the tension in the string T . The weight W acts vertically downwards at the center of mass of the rod, which is at a distance of L 2 from the hinge. The perpendicular distance of the line of action of W from the hinge is L 2 . The tension T acts horizontally at the upper end of the rod, which is at a distance L from the hinge. The perpendicul