Question

A rope is wound around a hollow cylinder of mass $3kg$ and radius $40cm$. The cylinder is hinged about its axis. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30N$?

• A. $5m/s^2$
• B. $25m/s^2$
• C. $0.25rad/s^2$
• D. $25rad/s^2$

Answer 1

The correct option is D $25rad/s^2$

$\text{Step 1: Free Body Diagram}$ $\text{[Refer Fig.]}$

$\text{Step 2: Torque equation}$

Applying torque equation about centre of cylinder

$\sum \tau =I\alpha$

$\tau =FR=I\alpha$

$I=$ moment of Inertia about center $=\frac{m{R}^2}{2}$

$\Rightarrow \alpha =\frac{FR}{I}=\frac{FR}{\left(\frac{m{R}^2}{2}\right)}=\frac{2F}{mR}$

$\text{Step 3: Calculations}$

$\alpha =\frac{2\times 30\left(N\right)}{3\left(kg\right)\times 0.4\left(m\right)}$

$\Rightarrow \alpha =25rad/r^2$

Hence, the correct option is $D$.