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  • A bead of mass slides along a straight frictionless rigid wire rotating in a horizontal plane with a

A bead of mass \mathrm{m} slides along a straight frictionless rigid wire rotating in a horizontal plane with a constant angular speed then the axes of rotation is perpendicular to the wire and \mathrm{p} asses through one end of the wire. If r is the distance of the mass from the axis of rotation and \mathrm{v} is its speed then the magnitude of Coriolis force is -
 

Option: 1

\mathrm{\frac{m v^2}{r}}
 


Option: 2

\mathrm{\frac{2 m v^2}{r}}
 


Option: 3

\mathrm{ mv\omega}
 


Option: 4

\mathrm{2mv\omega}


Answers (1)

best_answer

Use, \mathrm{\text { Coriolis force } =2 m \overrightarrow{\omega} \times \overrightarrow{v} }

                                     \mathrm{ =2 m \omega v \sin \theta }

since the axes of rotation is perpendicular to the wire.

\mathrm{ \theta=90^{\circ} }

\mathrm{ \therefore \text { coriolis force }=2 \mathrm{m\omega v} }

\mathrm{ \text { Since } \sin 90^{\circ}=1 }

Hence option 4 is correct.



 

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