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 v0 of the centre of the bobbin at the instant when the thread forms an angle a with the vertical.

Options:

A) vRRsinαr

B) vRRsinα+r

C) 2vRRsinα+r

D) vRsinα+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=v0sinαωr,

where v0sinα is the component of translational velocity along the thread ωr linear velocity due to rotation.

As the bobbin rolls without slipping, v0=ωR.

Solving the obtained equations, we get

v0=vRRsinαr



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