Question

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

A
5m/s2
B
25m/s2
C
D

Solution

## The correct option is D $$25\,rad/s^2$$$$\textbf{Step 1: Free Body Diagram}$$   $$\textbf{[Refer Fig.]}$$$$\textbf{Step 2: Torque equation}$$   Applying torque equation about centre of cylinder            $$\sum \tau =I\alpha$$                $$\tau=FR=I\alpha$$ $$I=$$ moment of Inertia about center $$=\dfrac{mR^2}{2}$$          $$\Rightarrow \,\alpha\,=\dfrac{FR}{I}=\dfrac{FR}{\left(\dfrac{mR^2}{2}\right)}=\dfrac{2F}{mR}$$$$\textbf{Step 3: Calculations}$$                                    $$\alpha =\dfrac{2\times 30(N)}{3(kg)\times 0.4(m)}\,$$               $$\Rightarrow \ \alpha = 25\,rad/r^2$$Hence, the correct option is $$D$$.Physics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More