Question

A ball on the end of a string is being swung in a vertical circle at a constant rate.
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. As two times in its circular path, the string is perfectly horizontal, 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
• E. As two times in its circular path, the string is perfectly horizontal, once on the way up and once on the way down. The tension in the string is greater on the way down than on the way up

Answer 1

Answer: (C)

As two times in its circular path, the string is perfectly horizontal, 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 $m\frac{v^2}{R}$ is same at all points. This is balanced by the gravitational force acting downwards and the tension acting on it towards the center.

At the top of the path,

$\frac{m{v}^2}{R}=T+mg$

$⟹T=\frac{m{v}^2}{R}-mg$

At the bottom of the path,

$T=\frac{m{v}^2}{R}+mg$

Correct answer is option C.