A simple pendulum of length L is released from rest from a horizontal position. During its downward swing, at a certain angle from the vertical, the net acceleration vector of the bob becomes purely horizontal. The value of is :

Step-by-step solution

Let the string make an angle with the vertical. Since the pendulum is released from the horizontal position, the vertical distance fallen by the bob is h = L . By conservation of mechanical energy, the velocity v of the bob is: 1 2 mv^2 = mgL v^2 = 2gL The centripetal acceleration is directed along the string towards the point of suspension: a_c = v^2 L = 2g The tangential acceleration is directed perpendicular to the string, downwards along the tangent: a_t = g For the net acceleration vector to be purely horizont