A force -`F` is applied at the topmost point of a cylinder of radius `r` and height `h`.
`(a)` If the cylinder remains at rest, then find distance of line of action of normal reaction from center of mass.
`(b)` Find coefficient of friction required so that the cylinder tooples before sliding.

Explanation

`(a)`
Since body is at rest, it is in translational equilibrium
`f_(r )=F`
For rotational equilibrium,
`tau_("net")=0` (about center)
`implies(Fxxh)/(2)+(Fxxh)/(2)-Na=0` (`:' f_(r )=F`)
`impliesa=(F*h)/(N)=(F*h)/(mg)`
`(b)`
For toppling about point `O`,
`tau_(F) gt tau_(mg)`
`impliesF.h gt mg .r`
`impliesF gt (mgr)/(h)`
To avoid sliding, `F lt mu mg`
Therefore, `(mgr)/(h) lt F lt mu mg`
`implies(r )/(h) lt mu`