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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, what is the condition for the mass to just complete the circular motion?

Options:

  1. Tension = 0
  2. Tension = mg
  3. Tension = 2mg
  4. Tension = mg/2

Correct Answer: Tension = 0

Solution: 

At the highest point, the centripetal force is provided by the weight of the mass, so T + mg = mv²/r. For T = 0, 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, what is the condition for the mass to just complete the circular motion?
  1. Tension = 0
  2. Tension = mg
  3. Tension = 2mg
  4. Tension = mg/2

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, what is the condition for the mass to just complete the circular motion?
Correct Answer: mg = mv²/r
  • Step 1: Understand that the mass m is moving in a vertical circle attached to a string.
  • Step 2: Identify the highest point of the circle where the mass is located.
  • Step 3: Recognize that at the highest point, two forces act on the mass: the weight of the mass (mg) acting downwards and the tension in the string (T) also acting downwards.
  • Step 4: Know that for the mass to stay in circular motion, there must be a net inward force (centripetal force) towards the center of the circle.
  • Step 5: Write 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 6: To find the condition for the mass to just complete the circular motion, consider the case where the tension T is zero (T = 0). This means the weight of the mass must provide all the necessary 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 can be rearranged to v² = g * r.
  • 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 mass due to gravity, which affects the motion of the mass at the highest point of the circle.
  • Tension in the String – The force exerted by the string on the mass, which can be zero at the critical point of completing the circular motion.
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