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

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

Options:

  1. T + mg
  2. T - mg
  3. T
  4. T + 2mg

Correct Answer: T + mg

Solution: 

At the bottom, T + mg = mv²/r; T = mv²/r - mg.

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

Practice Questions

Q1
A mass m is attached to a string and is whirled in a vertical circle. At the top of the circle, the tension in the string is T. What is the expression for the tension at the bottom of the circle?
  1. T + mg
  2. T - mg
  3. T
  4. T + 2mg

Questions & Step-by-Step Solutions

A mass m is attached to a string and is whirled in a vertical circle. At the top of the circle, the tension in the string is T. What is the expression for the tension at the bottom of the circle?
  • Step 1: Understand that the mass m is moving in a vertical circle, and we need to find the tension in the string at the bottom of the circle.
  • Step 2: At the top of the circle, the forces acting on the mass are the tension T and the weight of the mass mg (where g is the acceleration due to gravity).
  • Step 3: At the top, the centripetal force needed to keep the mass moving in a circle is provided by the tension and the weight. The equation is: T + mg = mv²/r, where v is the speed of the mass and r is the radius of the circle.
  • Step 4: Rearranging the equation from Step 3 gives us T = mv²/r - mg. This is the expression for tension at the top of the circle.
  • Step 5: Now, we need to find the tension at the bottom of the circle. At the bottom, the forces acting on the mass are the tension T and the weight mg, but this time the tension must provide the centripetal force.
  • Step 6: The equation at the bottom of the circle is: T - mg = mv²/r.
  • Step 7: Rearranging this equation gives us T = mv²/r + mg. This is the expression for tension at the bottom of the circle.
  • Centripetal Force – The net force acting on an object moving in a circular path, which is required to keep it 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 net force acting on an object, its mass, and its acceleration.
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