Question

A rigid body of mass m and radius r rolls without slipping on a rough surface. A force is acting on a rigid body x distance from the centre as shown in figure. Find the value of x so that static friction is zero.

• A. $\frac{I_{cm}}{mR}$
• B. $\frac{2I_{cm}}{mR}$
• C. $\frac{I_{cm}}{3mR}$
• D. $\frac{2I_{cm}}{3mR}$

Answer 1

The correct option is A $\frac{I_{cm}}{mR}$

Torque about centre of mass $Fx=I_{am}\alpha$............(i)
F = ma ..............(ii)
From eqn. (i) & (ii)
$max=I_{cm}\alpha (a=\alpha R)$
$x=$$\frac{I_{cm}}{mR}$