One end of a rope of length L is tied to a vertical pole. A man is pulling the rope with a constant force at its other end. Which point on the pole should the rope be tied at to uproot the pole most easily?

Explanation

Suppose the rope is tied at point B of the pole OA and is pulled by a force F from the other end C Fig. In order to uproot the pole, a rotational motion has to be set up about the base O of the pole. Moment of the force F about O sets up the rotation.
The moment = `FxxOD`
`=FxxBC sin theta`
`= FxxBC cos theta sintheta`
`=(1)/(2)F.Lsin2theta (because` BC =L)
The moment will be maximum when sin2 `theta` = 1 or, `theta= 45^(@)` .
Hence, OB = BC cos`theta= L cos 45^(@)=(L)/(sqrt(2))`
Hence, the rope should be tied at a height of `(L)/(sqrt(2))` from the ground.