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A man revolves a stone of mas s 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
Here T₁, T₂(and v₁, v₂) denote the tension in the string (and the speed of the stone) at the lowest and highest points, respectively.

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Lowest point Highest point

$mg - T_{1}$ $mg + T_{2}$

Lowest point Highest point

$mg + T_{1}$ $mg - T_{2}$

Lowest point Highest point

$mg + T_{1} - \frac{{mv}^{2}}{r}$ $mg - T_{2} + \frac{{mv}^{2}}{r}$

Lowest point Highest point

$mg - T_{1} - \frac{m_{1} v_{1}^{2}}{R}$ $mg + T + \frac{m_{1} v_{1}^{2}}{R}$

answer is A.

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Detailed Solution

$mg + T_{2} = \frac{{mv}_{2}^{2}}{R}, T_{1} - mg = \frac{{mv}_{1}^{2}}{R}$

Never confuse the actual force on a body (tension, force of gravity, etc.) with the effects they produce : $ma, \frac{{mv}^{2}}{R},$ etc.

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