A gardener presses the grasscutter with a force `F` at an angle `theta`. Assume the motion of grasscutter as pure rolling. Find the:

Maximum force F for no relative slidng if th coeficient of friction between the roller and ground is `mu`

Options

A. `(mumgcostheta)/(costheta+3musintheta)`
B. `(mumgsintheta)/(costheta+3musintheta)`
C. `(3mumg)/(costheta-3musintheta)`
D. `(3mumg)/(costheta+3musintheta)`

Answer

C

Explanation

`F costheta-f=ma` …………i
`fR=1/2mR^(2)alphaimpliesfR=1/2mR^(2)a/R`
`implies f=(ma)/2`………ii
From i and ii

`f=(Fcostheta)/3`
Now `a=(2f)/m=(2Fcostheta)/(3m)`
`flef_(1)implies(Fcostheta)/3lemuN`
`implies (Foscostheta)/3lemu(mg+Fsintheta)impliesFle(3mumg)/(costheta-3musintheta)`