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Question:

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 × 10⁻⁸ J by the end of the second revolution after the beginning of the motion?

0.18 m/s²

0.15 m/s²

0.2 m/s²

0.1 m/s²

Solution:

Energy, E = 1/2mv² ⇒ 8 × 10⁻⁸ = 1/2(10/1000)v² ⇒ v² = 16 × 10⁻⁶ ⇒ v = 4 × 10⁻³ = 0.4 m/s
Now, v² = u² + 2as
where, s = 4πr ⇒ 16 × 10⁻⁶ = 0 + 2at(4 × 22/7 × 6.4/100) ⇒ at = 0.1 m/s²