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 pulled with a force `F` as shown in the Fig. What is the maximum value of `F` for which the disc rolls without slipping ?

Options

A. `F_("max")=3 muMg`
B. `F_("max")=2 muMg`
C. `F_("max")=(1/2) muMg`
D. `F_("max")=4 muMg`

Answer

A

Explanation

Consider the diagram below
Frictional force (f) is acting in the opposite direction of F
Let the acceeleration of centre of mass of disc be a then
`F-F=Ma`
where M is mass of the disc

the angular acceleration of the disc is
`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`