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 masses of spring and pan are negligible. When pressed slightly and released, the mass executes SHM. 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 s⁻².)
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Question

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 masses of spring and pan are negligible. When pressed slightly and released, the mass executes SHM. 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 s⁻².)

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G1 Physics · Accepted Answer

Step 1: The object loses contact with the pan when the required downward acceleration at the top reaches g. Step 2: At the top of SHM, maximum downward acceleration = ω²A = (k/m)A. Step 3: At the threshold of detachment: (k/m)A = g, so A = mg/k. Step 4: Substitute m = 2 kg, g = 10 m s⁻² and k = 200 N m⁻¹: A = 20/200 = 0.10 m = 10.0 cm. Step 5: For actual separation, the amplitude must marginally exceed the threshold. Final answer: (A) 10.0 cm.