A stone with mass 0.8kg is attached to one end of a string 0.9m long . The string will break if its tension exceeds 600N. The stone is whirled in a horizontal circle ,the other end of the string remains fixed. Find the maximum speed , the stone can attain without breaking the string.

To find the maximum speed the stone can attain without breaking the string, we need to consider the tension in the string when the stone is at its maximum speed. At the maximum speed, the centripetal force acting on the stone is equal to the tension in the string.

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.

Sharma

m v^2/R = 600

0.8 v^2/0.9 = 600