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$$ g $$=$$ $$l0$$ $$m/s2)

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 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$$ g $$=$$ $$l0$$ $$m/s2)

Infinity Learn · Accepted Answer

Let the minimum amplitude of SHM is a.Restoring force on spring, F $$=$$ kaRestoring force is balanced by weight mg of block.For mass to execute simple harmonic motion of amplitude a.ka $$=$$ mg or a $$=$$ mgkHere, m $$=$$ $$2$$ kg, k $$=$$ $$200$$ $$N/m$$, g $$=$$ $$l0$$ $$m/s2a$$ $$=$$ $$2$$×$$10200$$ $$=$$ $$10100m$$ $$=$$ $$10100$$×$$100$$ cm $$=$$ $$10$$ cmHence, minimum amplitude of the motion should be $$l0$$ cm, so that the mass gets detached from the pan.

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