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A horizontal force F = 14 N acts at the ...

A horizontal force `F = 14 N` acts at the centre of mass of a sphere of mass `m = 1 kg`. If the sphere rolls without sliding, find the frictional force (in `N`)

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The correct Answer is:
4
FBD: the forces acting on the body are `Frarr mg darr` and `N uarr` and let us assume that `f` is backward `(larr)`
force equation
`F-f=ma`……..i
`N=mg=0`…………ii
torque equation:
`f.R=2/5mR^(2)alpha`
condition for rolling `a=Ralpha`……...iii
Putting a from eqn i `alpha` from eqn iii in eqn iv we have
` (F-f)/m=R.(5f)/(2mR)impliesf=2/7F=4N`
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