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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
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B
25m/s2
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C
0.25rad/s2
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D
25rad/s2
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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 $$D$$.

2107772_638346_ans_d06ec230dff040c4bc001af9caf240da.png

Physics

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