Concept:In physics problems involving a mass spun on a string in a vertical circle, questions usually imply the
minimum velocity required to complete the circle unless stated otherwise.
Formula:$$ T = \frac{mv^2}{r} - mg $$
Solution:- At the very top of the arc, both tension \( T \) and gravity \( mg \) point downward, providing centripetal force.
- If the object goes at the absolute minimum required velocity (\( v = \sqrt{gr} \)), substituting this into the equation yields: \( T = \frac{m(gr)}{r} - mg = mg - mg = 0 \).
- Thus, the critical minimum tension at the apex is exactly zero.
Why other options are incorrect:- Option B, Option C, Option D describe tension at other points (e.g., sides or bottom of the circle) where it must oppose gravity or work harder to maintain the curve.
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