# A uniform disc of radius R, is resting on a table on its rim.The coefficient of friction between disc and table is μ (Fig 7.12).

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A uniform disc of radius R, is resting on a table on its rim.The coefficient of friction between disc and table is μ (Fig 7.12). 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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Let the accelaration of the centre of mass of disc be ‘a’, then

Ma = F-f

The angular accelaration of the disc is a = a/R. (if there is no sliding).

Then

((1/2)MR2)α = Rf

⇒Ma = 2f

Thus, f = F/3. Since there is no sliding,

⇒ f ≤ μmg

⇒ F ≤ μMg.