Question

A rope is wound over on a solid cylinder of radius $0.1m$ and mass $10kg$. The cylinder is free to rotate about its fixed horizontal axis. If the rope is pulled with a force $10N$, then the angular acceleration of the cylinder is:

• A. $10rad/s^2$
• B. $5rad/s^2$
• C. $20rad/s^2$
• D. $14rad/s^2$

Answer 1

The correct option is C $20rad/s^2$

$I=\frac{10\times (0.1{)}^2}{2}$

$=0.05kg{m}^2$

$\tau =I\times \alpha =1.0Nm$

$\tau =I\alpha$

$1.0=\left(0.05\right)\alpha$

$\alpha =20rad/s^2$