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.

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., ∣ R s i n α − r v R ˉ ​ ∣, ∣ R s i n α + r v R ˉ ​ ∣, ∣ R s i n α + r 2 v R ˉ ​ ∣, ∣ R s i n α + r v R ˉ ​ ∣

MARKS App · Accepted Answer

When the thread is pulled, the bobbin rolls to the right. Resultant velocity of point B along the thread is ∣ v = v 0 ​ sin α − ω r ∣ , where ∣ v 0 ​ sin α ∣ is the component of translational velocity along the thread and ∣ ω r ∣ linear velocity due to rotation. As the bobbin rolls without slipping, ∣ v 0 ​ = ω R ∣ . Solving the obtained equations, we get ∣ v 0 ​ = R s i n α − r v R ​ ​

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