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Standard XII

Physics

Work Energy Theorem Application

The free end ...

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 a center of theybobbin at heh center at he instant when the thread forms an angle $α$ with the vertical.

\frac{v R}{R s i n α - r}

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\frac{v R}{R s i n α + r}

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\frac{2 v R}{R s i n α + r}

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\frac{v}{R s i n α + r}

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Solution

The correct option is A $\frac{v R}{R s i n α - r}$
The free end of a thread would on a bobbin is passed round a nail
A hammer into the wall.
The thread is pulled at a constant velocity.
Assuming pure rolling of bobbin.
Finding the velocity $v_{0}$ of a centre of they bobbin at the centre at he instant when the thread forms an angle $= α$ with the vertical.
Vertical $= \frac{d i s t a n c e}{t i m e} = \frac{v R}{R sin α - r}$

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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 a center of theybobbin at heh center at he instant when the thread forms an angle α with the vertical.