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Question
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 can withstand a maximum tension of 200 N?
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Solution
Mass of the stone, m = 0.25 kg
Radius of the circle, r = 1.5 m
Number of revolution per second, `n = 40/60 = 2/3` rps
Angular velocity , `omega= v/r = 2pin`
The centripetal force for the stone is provided by the tension T, in the string, i.e.,
`T = F_"Centripetal"`
= `(mv^2)/r = mromega^2 = mr(2pin)^2`
`= 0.25 xx 1.5 xx (2xx3.14xx2/3)^2`
= 6.57 N
Maximum tension in the string, Tmax = 200 N
`T_"max"` = `(mv_" max"^2)/m`
`:.v_"max" = sqrt((T_max xx r)/m)`
` = sqrt((200xx1.5)/0.25)`
= `sqrt(1200)` = 34.64 m/s
Therefore, the maximum speed of the stone is 34 .64 m/s
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