A mass of 2.0 kg is put on a flat pan attached to a vertical spring… | NEET 2007 (AIPMT)

Q80NEET 2007 · AIPMTMedium

Velocity & Acceleration in SHM

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).

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Answer: (a)

The mass leaves the pan at the top when $\omega^2 A = g$ .
$\omega^2 = \dfrac{k}{m} = \dfrac{200}{2} = 100\text{ s}^{-2}$
$A = \dfrac{g}{\omega^2} = \dfrac{10}{100} = 0.1\text{ m} = 10\text{ cm}$
So the answer is (a) 10.0 cm.

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