Question

A uniform disc of radius $R$ and mass $m$ is resting on a table on its rim, the coefficient of friction between the disc and the table is $\mu$. 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?

• A. $2\mu mg$
• B. $3\mu mg$
• C. $4\mu mg$
• D. $\frac{1}{2}\mu mg$

Answer 1

Answer: (B)

$3\mu mg$

For translational motion:

$F-f=ma$...........(1)
For rotational motion:

$fR=I\alpha$
$fR=\frac{m{R}^2}{2}\times \frac{a}{R}$.......(2)

Form $eq{u}^n\left(1\right)\&\left(2\right)$

$f=\frac{mg}{2}$ $f=\mu mg=\frac{mg}{2}$

$ma=2\mu mg$

$F-\frac{mg}{2}=mg$

$F=\frac{3ma}{2}=\frac{3\times 2\mu mg}{2}$

$F=3\mu mg$