Question

A uniform solid sphere of mass 2 kg is placed on rough horizontal surface. If a constant force F is applied horizontally at height R/2 above the center line, then the value of minimum co-efficient of friction to support pure rolling will be

Answer 1

For translational motion: ma=F−f where f=μmg

Thus ma=F−μmg .......(1)

For rotational motion: net torque about O, τ=Iα

fR=

5

2

mR

2

(α) .........(2)

Also as the sphere does not slip, thus a=rα

Equation (2) becomes , μmgR=

5

2

mR

2

R

a

ma=

2

5

μmg

Put it in (1),

2

5

μmg=F−μmg

⟹F=

2

7

μmg