Chapter 5, Problem 1OQ

You revolve a ball around you in a horizontal circle at constant speed on a string, as shown here from above. Which path will the ball follow if you let go of the string when the ball is at point P?

To determine

You revalue a ball around you in a horizontal circle at a constant speed on a string, as shown here from above and the path the ball will take if you release the string.

Answer to Problem 1OQ

Solution:

When we let go of the string then there is no force acting in a horizontal plane, so after release, the ball moves with constant velocity in the horizontal direction as velocity just before we let go of the string but after that gravitational force start acting which pull the ball in downward direction, hence:

(e) path followed by the ball.

Explanation of Solution

Concept used: Newton’s first law

  $\begin{array}{l}{\displaystyle \sum {\text{F}}_{\text{x}}\text{=0}}\\ {\text{a}}_{\text{x}}\text{=0}\end{array}$

After release, the string-net force acting on the ball in the horizontal plane is zero, only gravitational force is acting on the ball which is vertically downward direction hence, in a horizontal plane $\text{a=0}$ , so ball continues with same horizontal velocity but due to gravitational force it is like a horizontal projectile motion.

Conclusion:

If we revalue a ball around me in a horizontal circle at a constant speed on a string, after the release of string ball fly off in a tangential direction to the circular loop.