A mass of $2.0 \mathrm{~kg}$ is put on a flat pan attached to a vertical spring fixed on the ground as shown…
A mass of $2.0 \mathrm{~kg}$ 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 $200 \mathrm{~N} / \mathrm{m}$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take $g=10 \mathrm{~m} / \mathrm{s}^2$ ).
$10.0 \mathrm{~cm}$
any value less than $12.0 \mathrm{~cm}$
$4.0 \mathrm{~cm}$
$8.0 \mathrm{~cm}$
Solution
For given condition
$\begin{aligned}
m g & =m \omega^2 a=K a \\
\Rightarrow \quad a & =\frac{m g}{k}=\frac{2 \times 10}{200} \\
& =0.1 \mathrm{~m}=10 \mathrm{~cm}
\end{aligned}$
*
