Question

A rope is wound round a hollow cylinder of mass $3kg$ and radius $40cm$. If the rope is pulled with a force of $30N$, the angular acceleration of the cylinder will be:

• A. $10rad{s}^{-2}$
• B. $15rad{s}^{-2}$
• C. $20rad{s}^{-2}$
• D. $25rad{s}^{-2}$

Answer 1

The correct option is D $25rad{s}^{-2}$

Equating the torque about the center of mass we have

$F\times r=I\alpha$

$30\times 0.4=m{r}^2\times \alpha$

or
$30\times 0.4=3\times 0.4\times 0.4\times \alpha$

$\alpha =25rad/s^2.$