A mass m = 1.0 kg is put on a flat pan attached to a vertical spring… | JEE Main 2013 (22 Apr, Shift 1)

Q75JEE Main 2013 · 22 APR · SHIFT 1Medium

Velocity & Acceleration in SHM

A mass $m = 1.0$ kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan? (Take $g = 10$ m/s $2$ ). The spring is stiff enough so that it does not get distorted during the motion.

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Answer: (a)

The mass tends to leave the pan when the downward acceleration at the top reaches $g$ : $\omega^2 A \ge g$ .
$\omega^2 = \dfrac{k}{m} = \dfrac{500}{1} = 500\text{ s}^{-2}$
$A \ge \dfrac{g}{\omega^2} = \dfrac{10}{500} = 0.02\text{ m} = 2\text{ cm}$
So the answer is (a) $A \ge 2.0$ cm.

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