A cylinder of weight `W` and raidus `R` is to be raised onto a horizontal step of height `h=R//3` as shown. A rope is wrapped around the cylinder and pulled horizontally. Assuming no slipping, find the minimum value of `F` to raise the cylinder.

Explanation

When the cylinder is about to be raised, reaction at `A` vanishes.
Taking torque about `P`
`F(2R-h)geWl`
`l=sqrt(R^(2)-(R-h)^(2))`
`=sqrt(R^(2)-(R-(R)/(3))^(2))`
`=sqrt(R^(2)-(4R^(2))/(9))=(sqrt(5)R)/(3)`
`2R-h=2R-(R)/(3)=(5R)/(3)`
`Fxx(5R)/(3)geWxx(sqrt5R)/(3)`
`Fge(W)/(sqrt5)`
`F_(min)=(W)/(sqrt5)`