A uniform disco of mass M and radius R, is resting on a table on its rim. The coeffecient of friction between disc and table is mu. Now the disc is pulled with a force F as shown in the figure. What is the maximum value of F for which the disc rolls without slipping?

A uniform disco of mass M and radius R, is resting on a table on its r

1.	A uniform disco of mass M and radius R, is resting on a table on its rim. The coeffecient of friction between disc and table is mu. Now the disc is pulled with a force F as shown in the figure. What is the maximum value of F for which the disc rolls without slipping?
Answer» `F_("max")=3 muMg` `F_("max")=2 muMg` `F_("max")=(1/2) muMg` `F_("max")=4 muMg` Solution : Considerthediagrambelow Frictionalforce (f)is actingin theoppositedirectionof F Lettheacceelerationofcentre of massof discbe a then `F-F=Ma` where M ismass of thedisc theangularaccelerationof thediscis `alpha=a//R ""("for pure rolling")` from`tau=//alpha` `implies fR=((1)/(2)MR^(2))alphaimpliesfR=((1)/(2)MR^(2))((a)/(R))` `implies Ma = 2F` ....(ii) from Eqs. (i) and (ii)we get `f=F//3[:' N=mg]` `:'fle MU N =mu mg` ` (F)/(3)lemuMgimpliesF le3mu Mg` `implies F_("max")=3 muMg`