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If the mass and speed of an object are held fixed, what happens to the radius of its circular path as the centripetal force applied to it increases?
AThe radius increases in direct proportion to the force
BThe radius stays the same regardless of the force
CThe radius decreases, producing a tighter curve
DThe radius becomes undefined once force is applied
Answer & Solution
Correct answer: C. The radius decreases, producing a tighter curve
1. Solving Fc = m*v^2/r for the radius gives r = m*v^2/Fc.
2. With mass and speed fixed, r is inversely proportional to Fc, so increasing the force shrinks the radius.
3. A large centripetal force therefore causes a small radius of curvature, meaning a tighter curve.
4. The radius does not grow with the force, stay fixed, or become undefined, since the inverse relationship r = m*v^2/Fc always gives a well defined, shrinking radius as Fc grows.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.3 Centripetal Force_
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