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
Fmax = 3 μ M g