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m v^2/R = 600
0.8 v^2/0.9 = 600
0.8 v^2/0.9 = 600
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F = Centripetal force
m = Mass of the stone
v = Velocity of the stone
r = Radius of the circle (length of the string)
In this case, the centripetal force is equal to the tension in the string, so we can write:
Tension = (m * v^2) / r
Now we can rearrange the formula to solve for the maximum speed:
v^2 = (Tension * r) / m
v = √((Tension * r) / m)
Substituting the given values into the formula, we have:
v = √((600 N * 0.9 m) / 0.8 kg)
v = √(540 Nm / 0.8 kg)
v = √675 m^2/s^2
v ≈ 25.98 m/s
Therefore, the maximum speed the stone can attain without breaking the string is approximately 25.98 m/s.