Q. 28 A uniform disc of radius R, is resting on a table on its rim. coefficient of friction between disc and table is μ (figure). 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?

Hint: for pure rolling α=a/R.
Step 1: Write the equation for translational motion.
 
Consider the diagram below
Frictional force (f) is acting in the opposite direction of
Let the acceleration of the center of mass to disc a then
                    F - f = Ma                     ...(i)
where M is the mass of the disc
                          
Step 2: Write the equation for pure rolling.
The angular acceleration of the disc is
α=a/RforpurerollingStep3:Writetheequationfortorque.fromτ=fR=(12MR2)αfR=(12MR2)(aR)Ma=2f...ii
Step 4: Find Fmaxbysovingtheequations.
from equations (i) and (ii), we get
 
f=F/3[N=Mg]
fμN=μMg
F3μMgF3μMg
Fmax=3μMg