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A mass m is attached to a string and is whirled in a vertical circle. At the hig

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Question: A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?

Options:

  1. T = mg
  2. T = mg - mv²/r
  3. T = mg + mv²/r
  4. T = mv²/r

Correct Answer: T = mg - mv²/r

Solution: 

At the highest point, T + mg = mv²/r, thus T = mg - mv²/r.

A mass m is attached to a string and is whirled in a vertical circle. At the hig

Practice Questions

Q1
A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
  1. T = mg
  2. T = mg - mv²/r
  3. T = mg + mv²/r
  4. T = mv²/r

Questions & Step-by-Step Solutions

A mass m is attached to a string and is whirled in a vertical circle. At the highest point of the circle, the tension in the string is T. What is the expression for T?
  • Step 1: Understand that the mass m is moving in a vertical circle and at the highest point, there are two forces acting on it: the tension in the string (T) and the weight of the mass (mg).
  • Step 2: Recognize that at the highest point, both the tension (T) and the weight (mg) contribute to the centripetal force needed to keep the mass moving in a circle.
  • Step 3: Write down the equation for centripetal force at the highest point: T + mg = mv²/r, where v is the speed of the mass and r is the radius of the circle.
  • Step 4: Rearrange the equation to solve for the tension (T). Start with T + mg = mv²/r.
  • Step 5: Subtract mg from both sides to isolate T: T = mv²/r - mg.
  • Step 6: Factor out m from the right side: T = m(v²/r - g).
  • Step 7: This gives you the expression for the tension T at the highest point of the circle.
  • Centripetal Force – The net force acting on an object moving in a circular path, which is required to keep the object moving in that path.
  • Forces in Circular Motion – Understanding how gravitational force and tension interact at different points in a vertical circular motion.
  • Newton's Second Law – The relationship between the forces acting on an object and its motion, particularly in circular motion.
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