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Given: Mass of particle, M = 10 g = 10/1000 kg. Radius of circle R = 6.4 cm. Kinetic energy E of particle = 8 × 10⁻⁴ J. Find acceleration a₁.

1. 0.1 m/s²
2. 0.2 m/s²
3. 0.4 m/s²
4. 0.8 m/s²

Correct answer: 0.4 m/s²

Solution

The centripetal acceleration is given by a₁ = v²/R. From kinetic energy, E = 0.5 * M * v², we find v² = 2E/M. Substituting values, v² = (2 * 8 × 10⁻⁴) / (10/1000) = 0.16. Then, a₁ = v²/R = 0.16 / 0.064 = 0.4 m/s².

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