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A man revolves a stone of mass \( m \) tied to the end of a string in a vertical circle of radius \( R \). The net forces at the lowest and highest points of the circle directed vertical downwards are
\begin{tabular}{ll} \multicolumn{1}{c}{ Lowest point } & Highest point \\ (1) \( m g-T_{1} \) & \( m g+T_{2} \) \\ (2) \( m g+T_{1} \) & \( m g-T_{2} \) \\ (3) \( m g+T_{1}-\frac{m v^{2}}{r} \) & \( m g-T_{2}+\frac{m v^{2}}{r} \) \\ (4) \( m g-T_{1}-\frac{m_{1} v_{1}^{2}}{R} \) & \( m g+T+\frac{m_{1} v_{1}^{2}}{R} \) \end{tabular}
Here \( T_{1}, T_{2} \) (and \( v_{1}, v_{2} \) ) denote the tension in the string (and the speed of the stone) at the lowest and highest points, respectively.
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