A V shaped rigid body has two identical uniform arms. What must be the angle between the two arms so that when the body is hung from one end, the other arm is horizontal?

Step-by-step solution

Let the length of each arm be l . For one arm to be horizontal, the total torque acting about O should be zero, thus O P = O Q . Here the angle is θ between the two arms. From the figure, we have O Q = l 2 cos θ . As seen from the figure, A E = A C + C E A E = l cos θ + O Q l 2 = l cos θ + l 2 cos θ cos θ = 1 3 ⇒ θ = cos - 1 1 3