Question

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.

Answer 1

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)`