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  4. 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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Q. 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/s^{2})$Physics Question Image

AIIMSAIIMS 2007

Solution:

Let the minimum amplitude of SHM is $a$. Restoring force on spring
$F=k a$
Restoring force is balanced by weight $m g$ of block. For mass to execute simple harmonic motion of amplitude $a$.
$\therefore k a=m g$
or $a=\frac{m g}{k}$
Here, $m=2\, kg,\, k=200\, N / m , g=10\, m / s ^{2}$
$\therefore a =\frac{2 \times 10}{200}=\frac{10}{100} m$
$=\frac{10}{100} \times 100\, cm =10\, cm$
Hence, minimum amplitude of the motion should be $10\, cm$, so that the mass gets detached from the pan.