The tension in the string revolving in a vertical circle with a mass $m$ at the end which is at the lowest pos

Question

The tension in the string revolving in a vertical circle with a mass $m$ at the end which is at the lowest position is:

Accepted Answer

1. **Identify Forces:** At the lowest point of a vertical circle, the forces acting on the mass $m$ are the tension ($T$) in the string acting upwards (towards the center) and the gravitational force ($mg$) acting vertically downwards.
2. **Newton's Second Law:** The net radial force towards the center provides the necessary centripetal force ($F_c = \frac{mv^2}{r}$) to maintain the circular path.
   $$ F_{net} = T - mg $$
3. **Equation of Motion:** Equating the net force to the centripetal force:
   $$ T - mg = \frac{mv^2}{r} $$
4. **Solve for Tension:**
   $$ T = \frac{mv^2}{r} + mg $$
   [Source 75]

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