A ball tied to a string is rotated clockwise with a constant speed as shown in the figure. At which point should the string be released, if the ball has to hit the target? (Assume gravity-free space)

A ball tied to a string is rotated clockwise with a constant speed as shown in the figure. At which point should the string be released, if the ball has to hit the target? (Assume gravity-free space) Correct Answer B

The correct answer is option 2) i.e. B

CONCEPT:

• Uniform circular motion is where a moving object traces a circular path with constant speed.
  • ​A circle is assumed to be a polygon with infinitely many sides such that each side approximates to a point.
  • So, the object moving on a circular path undergoes a change in direction at every point.
  • Since direction changes and speed remains constant, velocity is varying.
• Centripetal acceleration: The acceleration associated with a change in velocity in a circular motion is called centripetal acceleration. It is directed towards the centre of the circular path.

EXPLANATION:

• The ball is under uniform circular motion, so it has a constant speed and varying velocity at every point on the circle.
• A circle is assumed to be a polygon with infinitely many sides such that each side approximates to a point. So the object moving on a circular path undergoes a change in direction at every point i.e. velocity vector will be directed tangentially to the point.
• If the string is released, the centripetal acceleration facilitating the circular motion is no more present.
• If the given ball has to hit the target, the velocity vector must be directed toward the target. For this, the string must be released at B.

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