The velocity of a body moving in a vertical circle of radius r is sqrt(7gr) at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

The velocity of a body moving in a vertical circle of radius r is sqrt

1.	The velocity of a body moving in a vertical circle of radius r is sqrt(7gr) at the lowest point of the circle. What is the ratio of maximum and minimum tension ?
Answer» `4:1` `sqrt(7):1` `3:1` ` 2:1` Solution :TENSION is maximum at the lowest point and minimum at the highest point. Tension at the lowest point, `T_L = mg + (mv_L^2)/(r) = mg + (7 mgr)/(r) = 8 mg "" ( :. v_L = sqrt(7 GR))` Tension at the highest point, `T_H = (mv_H^2)/(r) - mg = (m(v_L^2 - 4 gr))/(r) - mg ( :. v_L^2 - v_H^2 = 4 gr)` `= (m(7 gr - 4 gr))/(r ) - mg = 3mg - mg = 2mg `. `:. (T_L)/(T_H) = 4/1 " or " (T_("max"))/(T_("min")) = 4/1` .