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A child swings a ball attached to a string in a horizontal circle. If the radius

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Question: A child swings a ball attached to a string in a horizontal circle. If the radius of the circle is 2 m and the ball has a mass of 0.5 kg, what is the tension in the string if the ball moves at a speed of 4 m/s?

Options:

  1. 2 N
  2. 4 N
  3. 8 N
  4. 10 N

Correct Answer: 8 N

Solution: 

Tension provides the centripetal force: T = mv²/r = 0.5 kg * (4 m/s)² / 2 m = 8 N.

A child swings a ball attached to a string in a horizontal circle. If the radius

Practice Questions

Q1
A child swings a ball attached to a string in a horizontal circle. If the radius of the circle is 2 m and the ball has a mass of 0.5 kg, what is the tension in the string if the ball moves at a speed of 4 m/s?
  1. 2 N
  2. 4 N
  3. 8 N
  4. 10 N

Questions & Step-by-Step Solutions

A child swings a ball attached to a string in a horizontal circle. If the radius of the circle is 2 m and the ball has a mass of 0.5 kg, what is the tension in the string if the ball moves at a speed of 4 m/s?
  • Step 1: Identify the given values. The radius of the circle (r) is 2 meters, the mass of the ball (m) is 0.5 kilograms, and the speed of the ball (v) is 4 meters per second.
  • Step 2: Write down the formula for centripetal force, which is provided by the tension in the string. The formula is T = mv²/r.
  • Step 3: Substitute the values into the formula. Replace m with 0.5 kg, v with 4 m/s, and r with 2 m.
  • Step 4: Calculate v² (4 m/s)² = 16 m²/s².
  • Step 5: Multiply m (0.5 kg) by v² (16 m²/s²): 0.5 kg * 16 m²/s² = 8 kg·m/s².
  • Step 6: Divide the result by r (2 m): 8 kg·m/s² / 2 m = 4 N.
  • Step 7: The tension in the string is equal to the centripetal force, which is 8 N.
  • Centripetal Force – The force required to keep an object moving in a circular path, directed towards the center of the circle.
  • Tension in a String – The force exerted by a string or rope when it is pulled tight by forces acting from opposite ends.
  • Newton's Second Law – The relationship between the force acting on an object, its mass, and its acceleration (F = ma).
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