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 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 M/m. What should be the minimum amplitude of the motion so that the mass gets detached the pan? [Take $g=10m/s^2$]

• A. 10.0 cm
• B. Any value less than 12.0 cm
• C. 4.0 cm
• D. 8.0 cm

Answer 1

The correct option is A 10.0 cm

Let the minimum amplitude for which the mass will not detach from the pan be $a$. The restoring force at displacement equal to amplitude is $=ka$. The weight will not detach from pan if at this displacement the restoring force is balance by the weight of mass $\therefore mg=ka$

Or, $a=\frac{mg}{k}$

Here, given $m=2kg,g=10m/s^2,k=100N/m$

So, $a=\frac{2\times 10}{200}=0.1m=10cm$