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The velocity of a body moving in a verti...

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 ? 

A

`4:1`

B

`sqrt(7):1`

C

`3:1`

D

` 2:1`

Text Solution

Verified by Experts

The correct Answer is:
A
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` .
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