Final answer:
The tension in the string at the lowest point is 30 N.
Step-by-step explanation:
To find the tension in the string at the lowest point of the vertical circle, we need to consider the forces acting on the 5-kg mass. At the lowest point, the tension in the string provides the centripetal force, which is given by the equation T = mv^2/r, where T is the tension, m is the mass, v is the velocity, and r is the radius. In this case, m = 5 kg, v = 3 m/s, and r = 1.5 m. Plugging in these values, we get T = (5 kg)(3 m/s)^2 / 1.5 m = 30 N.