Consider a variation of the previous problem (figure). Suppose th… - Vidyadip

Question

Consider a variation of the previous problem (figure). Suppose the circular loop lies in a vertical plane. The rod has a mass m. The rod and the loop have negligible resistances but the wire connecting O and C has a resistance R. The rod is made to rotate with a uniform angular velocity $\omega$ in the clockwise direction by applying a force at the midpoint of OA in a direction perpendicular to it. Find the magnitude of this force when the rod makes an angle $\theta$ with the vertical.

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Answer

We know
$\text{F}=\frac{\text{B}^2\text{a}^3\omega}{2\text{R}}=\text{il}\text{B}$
Component of mg along $\text{F}=\text{mg } \sin \theta$
Net force $=\frac{\text{B}^2\text{a}^3\omega}{2\text{R}}-\text{mg }\sin\theta$

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