A stone of mass `0.25` kg tied to the end of a string is whirled round in a circle of radius `1.5` m with a speed of 40 rev/min in a horizontal plane . What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string ? What is the maximum speed with which the stone can be whirled around if the string can whirled around if the string can whirled around if the string can withstand a maximum tension of 200 N ?

Explanation

Here , m = 0.25 kg , r = 1.5 m
`n = 40 , rpm = 40/60 , rps = 2/3 ,T = ?`
`T = mrw^(2) = mr(2 pi n)^(2) = 4 pi^(2)m^(2)`
`T = 4xx (22/7)^(2) xx 0.25 xx 1.5 xx (2/3)^(2) = 6.6 N `
If `T_(max) = 200 N , ` then from
`T_(max) = (mv_(max)^(2))/r`
`v_(max)^(2) = (T_(max)xx r)/m = (200 xx1.5)/(0.25) = 1200`
`v_(max)=sqrt(200) = 34.6 m//s `