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A ball is tied to a string and swung in a vertical circle. At the highest point

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Question: A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?

Options:

  1. Tension = 0
  2. Tension = mg
  3. Tension > mg
  4. Tension < mg

Correct Answer: Tension = 0

Solution: 

At the highest point, the centripetal force is provided by the weight, so T + mg = mv²/r, T = 0.

A ball is tied to a string and swung in a vertical circle. At the highest point

Practice Questions

Q1
A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
  1. Tension = 0
  2. Tension = mg
  3. Tension > mg
  4. Tension < mg

Questions & Step-by-Step Solutions

A ball is tied to a string and swung in a vertical circle. At the highest point of the circle, what is the condition for the ball to just maintain circular motion?
Correct Answer: T = 0
  • Step 1: Understand that the ball is moving in a circle and needs a force to keep it moving in that circle.
  • Step 2: Recognize that at the highest point of the circle, two forces act on the ball: the tension in the string (T) and the weight of the ball (mg).
  • Step 3: Know that the weight of the ball (mg) acts downwards, while the tension (T) also acts downwards at the highest point.
  • Step 4: Realize that the total force acting downwards (T + mg) must provide the necessary centripetal force to keep the ball moving in a circle.
  • Step 5: Write the equation for centripetal force: T + mg = mv²/r, where m is the mass of the ball, v is the velocity, and r is the radius of the circle.
  • Step 6: For the ball to just maintain circular motion at the highest point, the tension (T) can be zero. This means the weight alone must provide the centripetal force.
  • Step 7: Substitute T = 0 into the equation: 0 + mg = mv²/r.
  • Step 8: Simplify the equation to find the condition: mg = mv²/r, which shows that the weight must equal the required centripetal force.
  • Centripetal Force – The net force required to keep an object moving in a circular path, directed towards the center of the circle.
  • Gravitational Force – The force acting on the ball due to gravity, which contributes to the centripetal force at the highest point of the circle.
  • Tension in the String – The force exerted by the string on the ball, which can be zero at the highest point if the ball is just maintaining circular motion.
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