Question

A ball at the end of a string is being swung in a vertical circle at a constant velocity. Which of these statements about the forces acting on the ball and the acceleration of the ball are true?

• A. The tension in the string at the top of its circular path and the bottom of its circular path are equal in magnitude.
• B. At the bottom of the circular path, the tension in the string acts up while the acceleration of the ball is down.
• C. The string is perfectly horizontal two times in the circular path, once on the way up and once on the way down. The only difference in the net force between these situations is the direction of the tension force.
• D. At the top of its circular path, the tension in the string acts down while the acceleration of the ball is up

Answer 1

The correct option is C The string is perfectly horizontal two times in the circular path, once on the way up and once on the way down. The only difference in the net force between these situations is the direction of the tension force.

Since the ball rotates in circle at constant rate, the speed of ball at all points is the same. Hence the centripetal force $\frac{m{v}^2}{R}$ is same at all points. This is provided by the gravitational force acting downwards and the tension acting on it towards the center. Acceleration of the ball is always radially inward (towards the centre)

At the top of the path,
$\frac{m{v}^2}{R}=T+mg$
$\Rightarrow T=\frac{m{v}^2}{R}-mg$
At the bottom of the path,
$T=\frac{m{v}^2}{R}+mg$
When the spring is horizontal, tension will be equal to centripetal force, only its direction will be opposite in the two cases (when it is going up and when it is coming down)
So, option c is correct.