Question

A uniform disc of mass M and radius R, is resting on a table on its rim. The coefficient of friction between disc and 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. Mg
• B. 2$\mu$ Mg
• C. 3$\mu$Mg
• D. 4$\mu$Mg

Answer 1

Answer: (C)

3$\mu$Mg

Answer 2

Let a be the acceleration of the centre of mass of disc. Then

Ma = F = f …(i)

If there is no slipping, angular acceleration ofj the disc.

….(ii)

Now torque of the disc

or

$\mathrm { I } = \frac { 1 } { 2 } \mathrm { MR } ^ { 2 }$

(using (ii))

Substituting this in Eq. (i), we get,

or

Since there is no slipping,

$\therefore \mathrm { f } \leq \mu \mathrm { Mg } \Rightarrow \mathrm { F } \leq 3 \mu \mathrm { Mg }$