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The tension in the string of a mass $m$ revolving in a vertical circle at the lowest position is

1. $m\dfrac{v^2}{r}$
2. $m\dfrac{v^2}{r}-mg$
3. $m\dfrac{v^2}{r}+mg$
4. $mg$

Correct answer: $m\dfrac{v^2}{r}+mg$

Solution

At the lowest point, tension acts upward toward the center and weight acts downward. The net upward force must provide centripetal force, so $T-mg=mv^2/r$, giving $T=mv^2/r+mg$.

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