Question

A massless stick of length L is hinged at one end and a mass m attached to its other end. The stick is free to rotate in vertical plane about a fixed horizontal axis passing through frictionless hinge. The stick is held in a horizontal position. At what distance x from the hinge should a second mass M = m be attached to the stick, so that stick falls as fast as possible when released from rest

A. `sqrt(2)L`
B. `sqrt(3)L`
C. `(sqrt(2)-1)L`
D. `(sqrt(3)-1)L`

Answer 1

Angular acceleration or rod
`alpha=(m(x+L)g sin theta)/(m(x^(2)+L^(2)))`
For rod to fall as fast as possible, `(dalpha)/(dx)=0`
or ` x=(sqrt(2)-1)L`