To determine the tension in the string, we can use the centripetal force equation, which states that the tension in the string provides the necessary centripetal force to keep the object moving in a circular path. The formula for centripetal force is given by:
F = m * (v^2 / r)
Where: F is the centripetal force m is the mass of the object (200g = 0.2kg) v is the velocity of the object (4 rad/s) r is the radius of the circular path (50cm = 0.5m)
Plugging in the values into the formula, we get:
F = 0.2kg * (4 rad/s)^2 / 0.5m = 0.2kg * 16 rad^2/s^2 / 0.5m = 0.2kg * 32 rad^2/s^2 / m = 6.4 N
Therefore, the tension in the string is 6.4 Newtons.