A solid cylinder wheel of mass `M` and radius `R` is pulled by a force `F` applied to the centre of the wheel at `37^@` to the horizontal. If the wheel is to roll without slipping, what is the maximum value of `|F|` ? The coefficients of static and kinetic friction are `mu_(s)=0.40` and `m_(k)=0.30. (sin37^@=3/5)`

Explanation

`FBD` is shown in figure

`N=Mg=-(3F)/5=Mg-0.6F`
For pure rolling `a=Ralpha`
or `(0.8F-mu_(s)N)/M=((R)(mu_(s)N)(R))/(1/2MR^(2))=(2mu_(s)N)/M`
`:. 0.8F=3(0.4)(Mg-0.6F)`
or `F=0.79Mg`
Therefore maximum value of `F` is `0.76 Mg`.