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Question
A uniform disc of radius R, is resting on a table on its rim.The 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?
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Solution
Let the acceleration of the centre of mass of the disc be ‘a’, then
`Ma = F - f` ......(1)
The angular acceleration of the disc is `α = a/R`. (if there is no sliding).
Then `(1/2 MR^2)α = Rf` ......(2)
⇒ `Ma = 2f`
Thus, `f = F/3`. Since there is no sliding,
⇒ `f ≤ µmg`
⇒ `F ≤ 3µMg`.
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