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A stone is tied to a string and whirled in a horizontal circle. If the radius of

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Question: A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to keep the stone moving in a circle at the same speed?

Options:

  1. It doubles
  2. It remains the same
  3. It halves
  4. It quadruples

Correct Answer: It halves

Solution: 

Centripetal force (F_c) = mv²/r. If r is doubled, F_c is halved for the same speed.

A stone is tied to a string and whirled in a horizontal circle. If the radius of

Practice Questions

Q1
A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to keep the stone moving in a circle at the same speed?
  1. It doubles
  2. It remains the same
  3. It halves
  4. It quadruples

Questions & Step-by-Step Solutions

A stone is tied to a string and whirled in a horizontal circle. If the radius of the circle is doubled, what happens to the centripetal force required to keep the stone moving in a circle at the same speed?
Correct Answer: Centripetal force is halved.
  • Step 1: Understand that centripetal force (F_c) is needed to keep an object moving in a circle.
  • Step 2: The formula for centripetal force is F_c = mv²/r, where m is mass, v is speed, and r is the radius of the circle.
  • Step 3: Identify that if the radius (r) is doubled, we replace r in the formula with 2r.
  • Step 4: Rewrite the formula with the new radius: F_c = mv²/(2r).
  • Step 5: Notice that when we double the radius, the formula shows that the centripetal force is now half of what it was before.
  • Step 6: Conclude that if the radius is doubled, the centripetal force required to keep the stone moving at the same speed is halved.
  • Centripetal Force – Centripetal force is the force required to keep an object moving in a circular path, which depends on the mass of the object, the speed of the object, and the radius of the circle.
  • Effect of Radius on Centripetal Force – Doubling the radius of the circular path while maintaining the same speed results in a decrease in centripetal force, as it is inversely proportional to the radius.
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