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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 minimum speed required to keep the mass in circular motion?

Options:

  1. √(g*r)
  2. g*r
  3. 2g*r
  4. g/2

Correct Answer: √(g*r)

Solution: 

At the highest point, the centripetal force is provided by the weight. Minimum speed = √(g*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 minimum speed required to keep the mass in circular motion?
  1. √(g*r)
  2. g*r
  3. 2g*r
  4. g/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 minimum speed required to keep the mass in circular motion?
  • Step 1: Understand that when an object is whirled in a circle, it needs a force to keep it moving in that circle. This force is called centripetal force.
  • Step 2: At the highest point of the circle, the only force acting on the mass that can provide this centripetal force is its weight (the force due to gravity).
  • Step 3: The weight of the mass is calculated using the formula: Weight = m * g, where 'm' is the mass and 'g' is the acceleration due to gravity (approximately 9.81 m/s²).
  • Step 4: For the mass to stay in circular motion at the highest point, the centripetal force needed is given by the formula: Centripetal Force = (m * v²) / r, where 'v' is the speed and 'r' is the radius of the circle.
  • Step 5: At the minimum speed, the weight of the mass will equal the centripetal force required to keep it moving in a circle. So, we set the two forces equal: m * g = (m * v²) / r.
  • Step 6: We can simplify this equation by canceling 'm' from both sides (as long as m is not zero): g = v² / r.
  • Step 7: To find the minimum speed 'v', we rearrange the equation: v² = g * r.
  • Step 8: Finally, we take the square root of both sides to find the minimum speed: v = √(g * r).
  • Centripetal Force – The force required to keep an object moving in a circular path, which at the highest point is provided by the gravitational force acting on the mass.
  • Minimum Speed in Circular Motion – The minimum speed at the highest point of a vertical circle is derived from the balance of forces, ensuring that the gravitational force is sufficient to provide the necessary centripetal force.
  • Gravitational Force – The force acting on the mass due to gravity, which is equal to m*g, where g is the acceleration due to gravity.
  • Radius of Circular Motion – The distance from the center of the circular path to the mass, which affects the required speed for maintaining circular motion.
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