Vertical Circle — Tension RatioHardQuestion 30641
Question
A ball (mass m) moves in a vertical circle (radius r). Speed at bottom = √(7gr). Tension at bottom T_b and at top T_t. T_b − T_t =
- A6mgCorrect
- B8mg
- C4mg
- Dmg
Correct answer
6mg
Explanation
T_b = m(v_b²/r + g) = m(7g+g) = 8mg. v_t² = v_b² − 4gr = 7gr−4gr = 3gr. T_t = m(v_t²/r − g) = m(3g−g) = 2mg. T_b − T_t = 8mg − 2mg = 6mg. (Note: T_b−T_t is always 6mg for vertical circles!)