Final answer:
To find the minimum period required to keep a mass moving in a circle, we need to consider the forces acting on the mass. By using the formula for tension and simplifying the equation, we can solve for the minimum period. In this case, the period is approximately 1.03 seconds.
Step-by-step explanation:
To find the minimum period required to keep the mass moving in a circle, we need to consider the force of gravity and the tension in the string. The tension in the string provides the centripetal force necessary to keep the mass in circular motion. The minimum period is the time it takes for the mass to complete one full revolution or cycle.
Using the formula for the tension in the string, T = (m*g) + (m*v^2/r), where m is the mass, g is the acceleration due to gravity, v is the velocity, and r is the radius of the circle, we can solve for the minimum period. In this case, the mass is 2.5 x 10² g, the radius is 1.2 m, and the velocity is determined by the gravitational force and the radius.
By simplifying the equation and substituting the values, we get T = (m*g) + (m*(2πr/T)^2/r), where T is the period. Solving for T, we find that the minimum period required to keep the mass moving in the circle is approximately 1.03 seconds.