Question

A hollow cylinder of mass $M$ and radius $R$ is pulled by a horizontal force $F$ acting at its centre of mass on a horizontal surface where the coefficient of friction is $\mu$.

If hollow cylinder is performing pure rolling then frictional force $f$ will be :

• A. $F$
• B. $\frac{F}{2}$
• C. $\frac{F}{3}$
• D. $2F$

Answer 1

The correct option is B $\frac{F}{2}$

There are two horizontal force on the hollow cylinder. One is friction force and other is $F$, in opposite direction. Taking the torque around top point ( there will be one pseudo force but that would pass via top point so there will no effect of that force in torque) .
Then, net torque around top point $=0$
$F\times R-f\times 2R=0$
$f=\frac{F}{2}$