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A stone of mass $\mathrm{m}$ tied to the end of a string is revolves in a vertical circle of radius $R$. The net force at the lowest and highest points of the circle directed vertically downwards are : (Choose the correct alternative).
$\begin{array}{ll}\text { Lowest Point } & \text { Highest Point } \\ \text { (a) } m g-T_1 & m g+T_2 \\ \text { (b) } m g+T_1 & m g-T_2 \\ \text { (c) } m g+T_1-\left(m v_1^2\right) / R & m g-T_2+\left(m v_1^2\right) / R \\ \text { (d) } m g-T_1-\left(m v_1^2\right) / R & m g+T_1+\left(m v_1^2\right) / R\end{array}$
$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.
$\begin{array}{ll}\text { Lowest Point } & \text { Highest Point } \\ \text { (a) } m g-T_1 & m g+T_2 \\ \text { (b) } m g+T_1 & m g-T_2 \\ \text { (c) } m g+T_1-\left(m v_1^2\right) / R & m g-T_2+\left(m v_1^2\right) / R \\ \text { (d) } m g-T_1-\left(m v_1^2\right) / R & m g+T_1+\left(m v_1^2\right) / R\end{array}$
$T_1$ and $v_1$ denote the tension and speed at the lowest point. $T_2$ and $v_2$ denote corresponding values at the highest point.
Solution:
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Verified Answer
The net force at the lowest point is $\left(m g-T_1\right)$ and the net force at the highest point is $\left(m g+T_2\right)$. Therefore, alternative (a) is correct.
Since $\mathrm{mg}$ and $T_1$ are in mutually opposite directions at lowest point and $\mathrm{mg}$ and $T_2$ are in same direction at the highest point.
Since $\mathrm{mg}$ and $T_1$ are in mutually opposite directions at lowest point and $\mathrm{mg}$ and $T_2$ are in same direction at the highest point.
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