A solid cylinder of mass `3 kg` is placed on a rough inclined plane of inclination `30^@`. If `g = 10 ms^(2)`, then the minimum frictional force required for it to roll without slipping down the plane is

Options

A. `2N`
B. `5N`
C. `15N`
D. `18N`

Answer

B

Explanation

`tau=fR=Ialpha` or `fR=1/2mR^(2)xxa/R`
or `f=1/2ma`………i
Now `mgsintheta-f=ma`
or `mgsintheta-=1/2ma=ma`
or `3/2ma=mgsintheta` or `1/2ma=(mgsintheta)/3`
From eqn if `f=(mgsintheta)/3`
Substituting values `f=(3xx10xx0.5)/3N=45N`