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 maintain the stone's circular motion 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 maintain the stone's circular motion 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: Know the formula for centripetal force: 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 dividing by 2r means 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 maintain the same speed is halved.
Centripetal Force – 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.
Relationship between Radius and Centripetal Force – Understanding how changes in the radius of the circular path affect the centripetal force required to maintain circular motion at a constant speed.
