Question

A unifrom disc of radius `R`, is resting on a table on its rim. The coefficient of friction between disc and table is `mu` Fig. Now the disc is spulled with a force `F` as shown in the Fig. What is the maximum value of `F` for which the disc rolls without slipping ?

Answer 1

Let `f` be the force of friction, when force applied is `F`.
If `a` is acceleration of the centre of mass of disc,
then `Ma = F - f` ..(i)
If there is no slipping, angular acceleration of disc, `alpha = (a)/(R )`.
Torque due to frictional force
`f xx R = I alpha = ((1)/(2)MR^(2))(a)/(R ) = (MaR)/(2) or Ma = 2f`
From (i), `2f = F - f or 3f = F or f = (F)/(3)`.
As there is no sliding, `f le mu Mg`
`:. (F)/(3) le mu Mg or F le3 mu Mg`
Hence, `F_(max) = 3 mu Mg`