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?
It doubles
It remains the same
It halves
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.
