To find the maximum speed the stone can attain without breaking the string, we need to determine the maximum tension the string can withstand.
We know that the tension in the string is equal to the centripetal force required to keep the stone moving in a circular path:
Tension = centripetal force = (mass x velocity^2) / radius
where the radius is the length of the string, 0.800 m.
If we rearrange the equation to solve for velocity, we get:
velocity = sqrt((Tension x radius) / mass)
Now we can substitute the given values:
Tension = 55.0 N (the maximum tension the string can withstand)
radius = 0.800 m
mass = 0.600 kg
Plugging these values into the equation, we get:
velocity = sqrt((55.0 N x 0.800 m) / 0.600 kg)
velocity = 3.31 m/s
Therefore, the maximum speed the stone can attain without breaking the string is 3.31 m/s.