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, ω = / = 2 ………………….(i)
The centripetal force for the stone is provided by the tension T, in the string, i.e.,
T = FCentripetal
= mv2/r = mrω2 = mr(2πn)2
= 6.57 N
Maximum tension in the string, Tmax = 200 N
Tmax = mv2max /r
vmax = √Tmax x r/m
= √200 x 1.5/0.25
= √1200 = 34.64 m/s
Therefore, the maximum speed of the stone is 34.64 m/s.