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). 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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Payal Gupta | Contributor-Level 10

4 months ago

This is a long answer type question as classified in NCERT Exemplar

Frictional force f is acting in the opposite direction of F . let the acceleration of centre of mass of disc be a then

F-f=Ma where M is the mass of the disc

$α = \frac{a}{R}$

$τ = I α$

fR= (1/2 MR²) $α$

so fR= (1/2MR²) (a/R)

Ma=2f

From the above equation

F = F/3

F< $μ N$ = $μ M g$

f/3 < $μ M g$

F=3 $μ M g$

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