A simple pendulum consists of a ball of mass `m` connected to a string of length `L`. The ball is pulled aside so that the string makes an angle of `53^(@)` with the verticle and is released. Find the ratio of the minumum and the tension in the string.

Explanation

The tension in the string is minimum when the ball is at the highest point and maximum when the ball is at the lowest point.
`v^(2)=u^(2)+2gh=0+2gL(1-cos53^(@))`
`=2gL(1-3//5)=(4gL)/(5)`
`T_(min)-mg cos 53^(@)=(m u^(2))/(L)=0`
`T_(min)-mgxx(3)/(5)impliesT_(min)=(3mg)/(5)`
`T_(max)-mg=(mv^(2))/(L)=(m)/(L).(4gL)/(5)`
`T_(max)=mg+(4mg)/(5)=(9mg)/(5)`
`(T_(min))/(T_(max))=(3)/(9)=(1)/(3)`