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A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s²)?

1. 10.0 cm
2. any value less than 12.0 cm
3. 4.0 cm
4. 8.0 cm

Correct answer: 4.0 cm

Solution

For the mass to detach from the pan, the spring force must equal the gravitational force acting on the mass. The spring force is given by F = kA, where k is the spring constant and A is the amplitude. Setting kA = mg, we get A = mg/k = (2 × 10) / 200 = 0.1 m = 10 cm. Thus, the minimum amplitude is 10 cm.

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