A uniform bar AB of mass m and length L is hinged at A and released from rest from the horizontal position. A ball of the same mass is released simultaneously from rest. Immediately after release, at what distance from end B is the point on the rod whose acceleration equals g?

Question

G1 Physics · Accepted Answer

For the rod, torque about A is mg(L/2) and I about A = mL²/3, so α = [mg(L/2)]/[mL²/3] = 3g/(2L). A point at distance x from A has tangential acceleration αx. Setting αx=g gives x=2L/3 from A, hence distance from B=L/3. Therefore option A.