Four particles have the following masses (in terms of m), speeds (in terms of v), and radii (in terms of r). Which particles have the same centripetal force as particle for which Fc=mv2/r?
Correct answer: B. Particle: 2, Mass: m/2, Speed: 2v, Radius: 2r
- A. Particle: 1, Mass: m, Speed: 4v, Radius: r
- B. Particle: 2, Mass: m/2, Speed: 2v, Radius: 2r
- C. Particle: 3, Mass: 2m, Speed: v/2, Radius: r
- D. Particle: 4, Mass: 1m, Speed: 2v, Radius: 3r
Explanation
To find particles with the same centripetal force as the given particle, we use the centripetal force formula Fc = (m × v2) / r. Particle-2, with mass m/2, speed 2v, and radius 2r, has a centripetal force Fc = (m/2× (2v)2) / (2r) = (mv2) / r, which matches that of particle.
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