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  • A heavy spool of inner radius '  ' and outer radius ' <img alt="20

A heavy spool of inner radius ' 10 \mathrm{~cm} ' and outer radius ' 20 \mathrm{~cm} ' is lying on a rough horizontal plane. Thread of negligible mass is wound over it and is being pulled with a constant force at an angle ' \alpha ' from the vertical as shown in the figure. Find the angle ' \alpha ' for which the centre of the spool remains at rest.

Option: 1

\frac{\pi}{6}


Option: 2

\frac{\pi}{3}


Option: 3

\frac{\pi}{4}


Option: 4

\frac{\pi}{2}


Answers (1)

best_answer

Making free body diagram of the spool:-

For translatory equilibrium :-

    \begin{aligned} & T \cos \alpha=M g \\ & T \sin \alpha=f \end{aligned}

For rotational equilibrium:-

\begin{gathered} f R=T r \\ f=\frac{T r}{R} \\ T \sin \alpha=\frac{T r}{R} \\ \sin \alpha=\frac{r}{R}=\frac{10 \mathrm{~cm}}{20 \mathrm{~cm}}=\frac{1}{2} \\ \alpha=\frac{\pi}{6} \end{gathered}

Posted by

Pankaj

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