Final answer:
The tension in a string when a ball is whirled in a vertical circle is the sum of the centripetal force and the ball's weight at the bottom of the circle, which can be calculated using the formula T = m(rω² + g), where m is the mass, r is the radius, ω is the angular velocity, and g is the acceleration due to gravity.
Step-by-step explanation:
The question pertains to the tension in a string when a ball is whirled in a vertical circle. According to physics principles, when the ball moves over the top of the circle at the slowest possible speed, the tension can be considered negligible. However, at the bottom of the circle, the tension in the string must provide the centripetal force required to keep the ball moving in a circle, while also countering the gravitational force acting on the ball. Hence, the tension will be greater at the bottom of the circle.
Analysis of Tension Forces
We have to consider two forces acting on the stone at the bottom of the vertical circle: the gravitational force (mg) and the centripetal force (mrω²), where 'm' is the mass of the stone, 'g' is the acceleration due to gravity, 'r' is the radius of the circular path, and 'ω' is the angular velocity of the stone.
The total tension in the string at this point will be the sum of the forces required for centripetal acceleration and the weight of the stone. Therefore, the formula for the tension at the bottom of the circle is:
Tension (T) = Centripetal force + Weight
T = m(rω² + g)
In scenarios like this, we would use the given values for mass, radius, and angular velocity to calculate the tension at specific points in the motion of the stone.