Question

A lawn roller in the form of a thin walled hollow cylinder of mass $M$ is pulled horizontally with a constant horizontal force $F$ applied by a handle attached to the axle. If it tolls without slipping.

• A. The frictional force $F/2$
• B. Acceleration is $F/2M$
• C. Acceleration is $F/M$
• D. The frictional force is $3F/4$

Answer 1

Answer: (A), (B)

The frictional force $F/2$
Acceleration is $F/2M$

$a=R\alpha$ (no slipping)

$fR=I\alpha$

$fR=M{R}^2\alpha$

$f=MR\alpha ⟹f=Ma$

Now $Ma=F-f$

$Ma=F-Ma⟹a=\frac{F}{2M}$

Thus $f=\frac{F}{2}$