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Topic: Uniform circular motion· Kinematics

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10^-4 J by the end of the second revolution aft…

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to \(8\times10^{-4}\) J by the end of the second revolution after the beginning of the motion ?

1. \(0.1\ m/s^2\)

2. \(0.15\ m/s^2\)

3. \(0.18\ m/s^2\)

4. \(0.2\ m/s^2\)

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Answer: 1. \(0.1\ m/s^2\)

Key idea: constant tangential acceleration \(a\) gives \(v^2=2as\) along the arc.

  1. \(\tfrac12mv^2=8\times10^{-4}\Rightarrow v^2=\dfrac{2\times8\times10^{-4}}{0.01}=0.16\) m\(^2\)/s\(^2\).
  2. Distance for two revolutions: \(s=2\times2\pi\times0.064\approx0.804\) m.
  3. \(a=\dfrac{v^2}{2s}=\dfrac{0.16}{1.608}\approx0.1\) m/s\(^2\).
Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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