A uniform bar AB of mass m and a ball of the same mass are released from rest form the same horizontal position. The bar is hinged at end A. There is gravity downwards. What is the distance of the point from point B that has the same acceleration as the ball, immediately after released ?

\(\frac{L}{3}\)

\(mg \frac{L}{2} = \frac{1}{3}mL^2 \alpha\)

\(\alpha = \frac{3g}{2L}\)

and \(\alpha x = g\)

\(\Rightarrow \frac{3g}{2L}x = g\)

\(x = \frac{2L}{3}\)

diatance from B : \(L - x = \frac{l}{3}\)