Question

A horizontal force $F$ is applied at the centre of mass of a cylindrical object of mass $m$ and radius $R$, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is $\mu$. The center of mass of the object has an acceleration $a$. The acceleration due to gravity is $g$. Given that the object rolls without slipping, which of the following statement(s) is(are) correct?

• A. For the same F, the value of $a$ does not depend on whether the cylinder is solid or hollow
• B. For a solid cylinder, the maximum possible value of $a$ is $2 \mu g$
• C. The magnitude of the frictional force on the object due to the ground is always $\mu mg$
• D. For a thin-walled hollow cylinder, $a=\frac{F}{2 m}$

Answer 1

Answer: (B), (D)

$F - f = ma $
$ fR = I \alpha $ (about center of mass)
$ a = R \alpha$ (pure rolling)
For hollow cylinder $a=\frac{F}{2 m}, f=\frac{F}{2}$
For solid cylinder, $a=\frac{2 F}{3 m}, f=\frac{F}{3}$
Also for solid cylinder $\frac{F}{2} \leq \mu\, mg$
Therefore a $\leq 2\, \mu g$