. 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?

vertical spring

(Tage g=10 m/s2)

(a)  8.0 cm       

(b)  10.0 cm

(c)  Any value less than 12.0 cm

(d)  4.0 cm


Best Answer

Ans: b

Solution: Let the minimum amplitude of SHM is a. Restoring force on spring

F = ka

Restoring force is balanced by weight mg of block. For mass to execute simple harmonic motion of amplitude a.

ka = mg

Or    a = mg/k

Here, m = 2g, k = 200 N/m, g = 10 m/s2

vertical spring

Hence, minimum amplitude of the motion should be 10 cm, so that the mass gets detached from the pan.





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