Q: A uniform disc of radius R, is resting on a table on its rim. The coefficient of friction between disc and table is μ . 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 ?

Sol: Let f be the frictional force acting on the disc .

F – f = M a ..(i)

As , τ = I α

$\displaystyle f R = \frac{M R^2}{2} \alpha $

$\displaystyle f R = \frac{M R^2}{2} (\frac{a}{R}) $

M a = 2 f ….(ii)

F – f = 2 f from(i)

f = F/3

f ≤ μ N

f ≤ μ N

f ≤ μ M g

$\displaystyle \frac{F}{3} \le \mu M g $

F ≤ 3 μ M g

F_{max} = 3 μ M g