If the radius of a circular path is doubled, how does the centripetal force chan

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Question: If the radius of a circular path is doubled, how does the centripetal force change for a constant speed?

Options:

Correct Answer: It halves

Solution:

Centripetal force F = mv²/r; if r is doubled, F is halved for constant speed.

If the radius of a circular path is doubled, how does the centripetal force change for a constant speed?

If the radius of a circular path is doubled, how does the centripetal force change for a constant speed?

Step 1: Understand the formula for centripetal force, which is F = mv²/r.
Step 2: Identify the variables in the formula: F is the centripetal force, m is mass, v is speed, and r is the radius of the circular path.
Step 3: Note that we are keeping the speed (v) constant while changing the radius (r).
Step 4: If the radius (r) is doubled, replace r in the formula with 2r: F = mv²/(2r).
Step 5: Compare the new force with the original force: F_new = mv²/(2r) is half of the original force F = mv²/r.
Step 6: Conclude that if the radius is doubled, the centripetal force is halved for constant speed.

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, its speed, and the radius of the circular path.
Relationship between Radius and Centripetal Force – The formula for centripetal force shows that for a constant speed, if the radius increases, the required centripetal force decreases.