Rotational Motion Question 222
Question: The free end of a thread wound on a bobbin is passed round a nail A hammered into the wall. The thread is pulled at a constant velocity. Assuming pure rolling of bobbin, find the velocity $v _{0}$ of the centre of the bobbin at the instant when the thread forms an angle a with the vertical.
Options:
A) $\frac{vR}{R\sin \alpha -r}$
B) $\frac{vR}{R\sin \alpha +r}$
C) $\frac{2vR}{R\sin \alpha +r}$
D) $\frac{v}{R\sin \alpha +r}$
Show Answer
Answer:
Correct Answer: A
Solution:
[a] When the thread is pulled, the bobbin rolls to the right.
Resultant velocity of point B along the thread is $v=v _{0}\sin \alpha -\omega r$,
where $v _{0}\sin \alpha $ is the component of translational velocity along the thread $\omega r$ linear velocity due to rotation.
As the bobbin rolls without slipping, $v _{0}=\omega R$.
Solving the obtained equations, we get
$v _{0}=\frac{vR}{R\sin \alpha -r}$
