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

Acceleration of `CM` of the roller (disc). Assume that the mass of the disc is `m` and neglect the mass of the connecting rod.

Options

A. `(2Fcostheta)/(3m)`
B. `(Fsintheta)/(3m)`
C. `(2Fsintheta)/(3m)`
D. `(Fcostheta)/(3m)`

Answer

A

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)`